Excellent explanation. What makes it so clear is that you "factor" the modified expression to show exactly why the 25 is in there. Most people don't include that part in the explanation. Understanding how and why is so much better than trying to memorise a series of stages that make no sense without context. Thank you.
Thank you so much!! I looked at like 5 different videos and none of them made any sense to me until this one!! All of the others just beat around the bush and did some weird method that took like ten minutes. I wished I could give 20 thumbs ups. You've got a new subscriber!
Great explanation! One thing I would add at the end. 32 is 16 * 2. Therefore, after the plus and minus we can put four times the square root of 2. That would be in a more simplified form.
THANK YOU! This helped me so much with studying for a test. No other video explained it like this and i was completely clueless. You explained it so well and made it so much easier to understand!!
You breaking it down is beautiful, thanks for the help. You're an angel! you didn't leave anything out and you answered ALL my questions thoroughly. sorry I'm 8 years late lol
Check out Mind Your Decision's explanation of quadratics using geometry. It visually shows "completing the square" making it concrete why you take half of b and square it. Really neat way to see it. This was still very good. Putting the two together is helpful.
They say a topic isn’t fully understand until the person can teach it, yep, this guy understands it, makes it look oh so simple 🙀🙀😳😩, is a really good video..
My gods. I was so confounded as to why we were doing all that stuff to b in ax^2+bx+c=0. I don't know how i didn't recognize the perfect square before! Why do so many math courses insist on just telling you how to get the right answer without explaining how it works or what the underlying concept is?! It makes so much sense now. I'm ashamed for not realizing it all right away. I wish i could give this video more than one thumbs up. My gods...
twistedblktrekie I've been homeschooling myself alone with books and online resources for over a year now. The internet and myself are the best teachers i've ever had. Math teachers would practically never explain anything. I went to a public school in a ghetto too, so, that also probably didn't help. I can hardly wait until i start calculus. I never imagined that i would actually love mathematics.
twistedblktrekie I learn in a similar way, but for me, if it doesn't make sense to me conceptually, i'll have more trouble recalling it, and i'll get frustrated, so, i usually don't move on until i understand the concept adequately at the very least (by my own judgement i suppose, but hey). Luckily, the concepts often aren't difficult for me to understand at all, but i'm only on algebra 2 right now. I desperately want to be a physicist. I don't know if i can, or if i can even get into a good university due to my past and the circumstances my past has put me in. But it's what i want anyway. I'm 19, so i'm already very behind too.
twistedblktrekie My mom is a nurse; knowing what i know, i would never ever get into medical. Physics is my dream. It has been since 1st grade. I'm just not giving up because there isn't much else i want out of life aside from that anyway, aside from my dogs and some video games. Money doesn't matter much to me as long as i have those 3 things and sustenance, basically.
twistedblktrekie Honestly, i only took half a course in quantum mechanics before i decided to stop and go learn the math first. But, that half a course changed the world in my eyes, and i feel like it's something i'd like to put my life into. I loved physics since first grade; i just didn't know it before about a year and a half ago. There are a lot of good physics courses online, and a lot of good books if you're interested. I personally would recommend the Feynman lectures firstly. Wish me luck... I'll probably have a hard time getting into a good university, but, i suppose i'm too dense to give up.
twistedblktrekie It depends. There are jobs in universities, in companies, and for the government. The university jobs are the best; and the most difficult to attain. I do not want to work for the government, but company jobs can vary greatly. I want to be able to do actual research though. I really need to get into a top school, at least for grad school. People who go to just any old university for a physics major seem to always end up in a cubicle farm doing work that their heart isn't in.
THANK YOU. Geezus. I'm a grown adult taking a business math class, and I'd forgotten how to factor that out. After two days of watching videos and reading books, this finally clicked for me. Thank you thank you thank you.
Completing The Square really makes sense when you see it done with the area model. It because obvious why the middle term is divided in 2 and squared. A Quadratic is a square, geometrically-speaking. The reason you divide the middle term in 2 is because each side lengths have to be the same. You square it because you are literally adding a missing square units (length X width) to the larger square to make it whole. One thing I've learned about math is the more you understand (concepts and mathematical logic), the less you have to memorize. Math is just the language of numbers. Good luck in school.
could you do a video about rational functions, equations, and inequalities i'm having a hard time dealing with complicated problems but you're videos always helps out. thank you very much :)
This is the most rationale explanation I have seen. Moreover, the narrative can be said to be measured, natural and straight to the point. Impressive way of reassuring learners whilst going through the steps in a clear and humble manner. In short, the video is about the subject and not about 'creating a personality or show' to pseudo entertain. Love this method of calm step by step explanation.Could there be a similar video, but of the type where the x squared term has a leading co-efficient?
Great to hear, thanks man. No I don't have any videos specifically about that, but you can always divide both sides of the equation by whatever the leading coefficient is to eliminate it. If you proceed from there with the same method, it won't be pretty but it'll work. Cheers
Thank you SO much. I am studying for my CSET and this is the only one that breaks it down the way that makes sense. I couldn't figure out what the point was in using Completing the Square when we can factor or use the Quadratic Equation. Other channels say "If a is equal to 1, add b/2 squared and it completely threw me off. But, what if a is not equal to 1?
OMGGGG THANK YOU IVE BEEN STUCK WITH THIS FOR 9HRS BUT NOW I UNDERSTAND GOD BLESS YOU I WAS ABOUT TO CHECK YOUR OTHER VIDEOS BUT YOU ONLY HAVE *VIDS WE NEED MORE PEOPLE LIKE YOUUUUUUU AAAA THANKASSASAS
@@stuartbowman_ Oh my gosh, I had thought you left, your tutoring level is so much better then anyone I find on youtube and they try to make it look cool with graphics but you doing it on paper really makes it feel like authentic maths! I wish you would come back
I can think of factors that multiply to give -7 and add to give 10: 5 + sqrt(32) 5 - sqrt(32) The point being, just cause something can't be factored using integers, it doesn't mean it can't be factored.
@@user-in9of6os2c ... yes... you have to move the end coefficient to the other side in order to make a perfect square on one side... but also note you have to add the new coefficient to both sides in order for the equation to balance. As you can see, he’s not done anything that unbalances the equation. Eg, he hasn’t added to one side, that he hasn’t done for the other... I hope that helps. The formula he gave is ‘B (middle coefficient of x) divided by 2 and squared’. So, half of 10 and squared = 25... then add 25 to both sides. Also remember, X is one side of the equation and Y is the other... on your graph, you have X axis, positive & negative, and Y axis, positive and negative.... thus a squared graph, and why the expression is completing the square. After you’ve solved the quadratic equation, for X & Y, you can then plot or plug in the numbers onto your graph... it looks hard, but when you know how and why it’s used, it’s actually a work of genius.
Thank you for taking the time to explain each step (even the "dumb" ones). Other videos we watched on this subject glossed over the "obvious" steps, making them impossible to follow (giving me flashbacks to some of the really bad math teachers I've had). My son was able to complete his math homework, thanks to you!
dude, thank you SO much! i was having a hard time with this and this totally helped! bonus points for also actually explaining how and why it works the way it does!
Thanks - very useful -- normally that '25' that you put in is put in as a fraction over 2, then brackets which are squared ... exactly the same thing, but o much more confusing when you don't really realise what's happening to/with that extra equation - this made it crystal clear :)
I'm looking at the comments in a bunch of videos and all these people seem like they are in a higher grade than me doing what I'm doing. I'm in 8th grade? What? I'm home schooled but someone pls answer my question. Why is this happening to me. Okay I'm done (btw u r better than my teacher)
if the coefficient of x is -10, will you still add +25 to both sides or will you will you apply -25 instead. i am refering to an equation that looks like this x^2-10x-7=0 ??? Thank you
Acellus needs to hire you. My daughter is so frustrated with math. Im so frustrated with my attempts to help her. Would you be upset it i wrote/spoke with the school about you?
What does solving a quadratic equation have to do with the real word? How would we get to the point where something physical was described by a quadratic equation?
Yes: sqrt(32)=sqrt(16*2)=sqrt(16)*sqrt(2)=4*sqrt(2). He probably left out the simplification so as not to distract from the main point of the video, but you make a good point.
Happy to see a teacher that can actually teach. Most teachers on youtube, or even at schools, do not know how to explain to students.
Excellent explanation. What makes it so clear is that you "factor" the modified expression to show exactly why the 25 is in there. Most people don't include that part in the explanation. Understanding how and why is so much better than trying to memorise a series of stages that make no sense without context. Thank you.
Deffinetly better than ur prof , straight to the point . It feels like a private lesson 😂😂😂
i have also explained this method in more easily .. watch on my youtube channel .. Tajamul Sir ..
I’ve just had a private lesson ,and still can’t do it
OH MY GOD THANK YOU. All the other videos didn’t make any sense. Bless your soul. Your username is true.
Hey
100% agreed thx so much BetterThanYourProf
why is this 480p vid lookin lik a 1080p one?
yup it looks like one
Shhhs dont complain,YT might screw us over if the find out
Simple colour palette, nothing to blur.
Haha I actually filmed this on my super old Droid RAZR. I really don't get it either :D
Thank you so much!! I looked at like 5 different videos and none of them made any sense to me until this one!! All of the others just beat around the bush and did some weird method that took like ten minutes. I wished I could give 20 thumbs ups. You've got a new subscriber!
You actually are better than all the professors I've had combined.
Great explanation! One thing I would add at the end. 32 is 16 * 2. Therefore, after the plus and minus we can put four times the square root of 2. That would be in a more simplified form.
THANK YOU! This helped me so much with studying for a test. No other video explained it like this and i was completely clueless. You explained it so well and made it so much easier to understand!!
U r actually better than my prof😂😂
LOL
You breaking it down is beautiful, thanks for the help. You're an angel! you didn't leave anything out and you answered ALL my questions thoroughly. sorry I'm 8 years late lol
There’s five methods actually...
Isolation
Quad formula
Diamond
Complete the square
Grouping
6. Giving up
@@benisman underrated comment
@@ayushkishor3207 for real
I just want 3 it's too much for me
Summer class Gaming WOAH TWO YEARS AGO LOL quadratics are easy as you get higher and higher in math
i love it. i like how you explain things so gentle for us to understand better thankyou
This video had all the steps explained carefully and well. It has really really helped me. THANK YOU !
what happens when your "B" value doesn't give a good number when dividing by 2? For example, what if the B value is 15 or 9 or 33?
Check out Mind Your Decision's explanation of quadratics using geometry. It visually shows "completing the square" making it concrete why you take half of b and square it. Really neat way to see it.
This was still very good. Putting the two together is helpful.
BEST EXPLANATION EVER♥️
They say a topic isn’t fully understand until the person can teach it, yep, this guy understands it, makes it look oh so simple 🙀🙀😳😩, is a really good video..
this video is 9 years old, wow i hope this person is doing well in life and im wishing them the best
I'm good :) So glad these videos are still useful to people
@@stuartbowman_ OHMYGOD,,, you replied! glad to hear that! and yes this was very helpful, thank you so much!
My gods. I was so confounded as to why we were doing all that stuff to b in ax^2+bx+c=0.
I don't know how i didn't recognize the perfect square before!
Why do so many math courses insist on just telling you how to get the right answer without explaining how it works or what the underlying concept is?!
It makes so much sense now. I'm ashamed for not realizing it all right away.
I wish i could give this video more than one thumbs up.
My gods...
twistedblktrekie I've been homeschooling myself alone with books and online resources for over a year now. The internet and myself are the best teachers i've ever had.
Math teachers would practically never explain anything. I went to a public school in a ghetto too, so, that also probably didn't help.
I can hardly wait until i start calculus. I never imagined that i would actually love mathematics.
twistedblktrekie I learn in a similar way, but for me, if it doesn't make sense to me conceptually, i'll have more trouble recalling it, and i'll get frustrated, so, i usually don't move on until i understand the concept adequately at the very least (by my own judgement i suppose, but hey).
Luckily, the concepts often aren't difficult for me to understand at all, but i'm only on algebra 2 right now.
I desperately want to be a physicist. I don't know if i can, or if i can even get into a good university due to my past and the circumstances my past has put me in. But it's what i want anyway. I'm 19, so i'm already very behind too.
twistedblktrekie My mom is a nurse; knowing what i know, i would never ever get into medical. Physics is my dream. It has been since 1st grade. I'm just not giving up because there isn't much else i want out of life aside from that anyway, aside from my dogs and some video games. Money doesn't matter much to me as long as i have those 3 things and sustenance, basically.
twistedblktrekie Honestly, i only took half a course in quantum mechanics before i decided to stop and go learn the math first. But, that half a course changed the world in my eyes, and i feel like it's something i'd like to put my life into. I loved physics since first grade; i just didn't know it before about a year and a half ago.
There are a lot of good physics courses online, and a lot of good books if you're interested. I personally would recommend the Feynman lectures firstly.
Wish me luck... I'll probably have a hard time getting into a good university, but, i suppose i'm too dense to give up.
twistedblktrekie It depends. There are jobs in universities, in companies, and for the government. The university jobs are the best; and the most difficult to attain. I do not want to work for the government, but company jobs can vary greatly. I want to be able to do actual research though.
I really need to get into a top school, at least for grad school. People who go to just any old university for a physics major seem to always end up in a cubicle farm doing work that their heart isn't in.
THANK YOU. Geezus. I'm a grown adult taking a business math class, and I'd forgotten how to factor that out. After two days of watching videos and reading books, this finally clicked for me. Thank you thank you thank you.
Completing The Square really makes sense when you see it done with the area model. It because obvious why the middle term is divided in 2 and squared. A Quadratic is a square, geometrically-speaking. The reason you divide the middle term in 2 is because each side lengths have to be the same. You square it because you are literally adding a missing square units (length X width) to the larger square to make it whole. One thing I've learned about math is the more you understand (concepts and mathematical logic), the less you have to memorize. Math is just the language of numbers. Good luck in school.
Thank you so much! I've watched so many videos and this was the only one that made sense! Thank yooooooou
Bruh this guy is a genius he deserves more subs
Seeing this video after 10 years but then also a life saver and by following the rules of algebra, this equates this video to a legend
#THANKS BRO#
THANK YOU SO MUCH. Your video was the only one that made any sense at all. You put Khan Academy to shame! ;) God bless you!!
Oooh so good!!!! Even at my higher level of study I still had issues but these video has helped me
So far I'm now good!!
Dude, you are literally a legend! tysm for the clear explanation, the best I could find on YT so far!
BRO, thank you! you saved me from getting a 1 hour detention!
you definitely better than my prof thaaaaaaaaaaaaaaannnnnnkkk yoooooooooooouuuuuuuuuuu
The best explanation so far
I know this is a relatively old video, nonetheless, I found it very helpful and was finally able to connect some concepts. Thank you.
heh
could you do a video about rational functions, equations, and inequalities i'm having a hard time dealing with complicated problems but you're videos always helps out. thank you very much :)
This is the most rationale explanation I have seen. Moreover, the narrative can be said to be measured, natural and straight to the point. Impressive way of reassuring learners whilst going through the steps in a clear and humble manner. In short, the video is about the subject and not about 'creating a personality or show' to pseudo entertain. Love this method of calm step by step explanation.Could there be a similar video, but of the type where the x squared term has a leading co-efficient?
Great to hear, thanks man. No I don't have any videos specifically about that, but you can always divide both sides of the equation by whatever the leading coefficient is to eliminate it. If you proceed from there with the same method, it won't be pretty but it'll work. Cheers
Best explanation on CZcams. I remember being confused on this when I was in 10th grade.
Im south africa and ive just subscribed and pressed d alert button. U d best man. Better dan those plastic professors LOL
Your lecture is quite intelligible, I'm very glad, thank you
You have no idea how much I love you
Thank you SO much. I am studying for my CSET and this is the only one that breaks it down the way that makes sense. I couldn't figure out what the point was in using Completing the Square when we can factor or use the Quadratic Equation. Other channels say "If a is equal to 1, add b/2 squared and it completely threw me off. But, what if a is not equal to 1?
Then you divide all the numbers by the a
FOR example 2x² + 10x = 0
You do 2x²/2 + 10x/2 = 0
You're welcome! Glad it made sense
OMGGGG THANK YOU IVE BEEN STUCK WITH THIS FOR 9HRS BUT NOW I UNDERSTAND GOD BLESS YOU I WAS ABOUT TO CHECK YOUR OTHER VIDEOS BUT YOU ONLY HAVE *VIDS WE NEED MORE PEOPLE LIKE YOUUUUUUU AAAA THANKASSASAS
i literally watched 40 videos prolly but this one is the only one i understood by watching it ONCE
√32 is reducible to 4√2.
I was wondering about that. Is it considered incorrect if the reduction is not completed?
@@leonelfederico245 i dont know
@@leonelfederico245 it's considered incorrect.
your S's sound like a blow off valve, good video clears all of the confusion i had up.
Dude the way you teach is fantastic… you really give thought to what some people may or may not know! Thank you so much!
Thanks! Back when I made these videos I was tutoring math every day so I had lots of practice
@@stuartbowman_ Oh my gosh, I had thought you left, your tutoring level is so much better then anyone I find on youtube and they try to make it look cool with graphics but you doing it on paper really makes it feel like authentic maths! I wish you would come back
If the leading coefficient is > or = 2, how would I go about solving the equation? Say 3x^2 - 12x + 9
You are the best mathermatics teacher
I'm so slow at learning this kind of stuff but when I saw this I got it straight away
I can think of factors that multiply to give -7 and add to give 10:
5 + sqrt(32)
5 - sqrt(32)
The point being, just cause something can't be factored using integers, it doesn't mean it can't be factored.
That is the best explanation of completing the square I've heard. Bless you sir!
"I can't think of any factors of 7..." It's a prime number!
@Matthew Bair Yeah, that' a Prime number.
Glad I could help
I just have one thing to ask why did you cancel the -7?
And like would that happen in like any question with completing the square
@@user-in9of6os2c ... yes... you have to move the end coefficient to the other side in order to make a perfect square on one side... but also note you have to add the new coefficient to both sides in order for the equation to balance. As you can see, he’s not done anything that unbalances the equation. Eg, he hasn’t added to one side, that he hasn’t done for the other... I hope that helps. The formula he gave is ‘B (middle coefficient of x) divided by 2 and squared’. So, half of 10 and squared = 25... then add 25 to both sides. Also remember, X is one side of the equation and Y is the other... on your graph, you have X axis, positive & negative, and Y axis, positive and negative.... thus a squared graph, and why the expression is completing the square. After you’ve solved the quadratic equation, for X & Y, you can then plot or plug in the numbers onto your graph... it looks hard, but when you know how and why it’s used, it’s actually a work of genius.
what if you had an equation where you have to divide by a negative like -4b=64
What if the linear term is negative when we are going to found the square root of it.Can I square root it even it's negative?
Thank you for taking the time to explain each step (even the "dumb" ones). Other videos we watched on this subject glossed over the "obvious" steps, making them impossible to follow (giving me flashbacks to some of the really bad math teachers I've had). My son was able to complete his math homework, thanks to you!
finding this video is the highlight of my quarantine
dude, thank you SO much! i was having a hard time with this and this totally helped! bonus points for also actually explaining how and why it works the way it does!
5:36 why is it -5 and how do you know when to make it -
Thanks for sharing your knowledge.
Thanks, You saved my life. Got yourself a new sub
Thank you!! Got straight to the point and was very informative :)
This is very helpful and easy to understand.
Your video really helped me I appreciate it thanks 🙏
Amazing job man you did a great job and helped me a lot
Thanks - very useful -- normally that '25' that you put in is put in as a fraction over 2, then brackets which are squared ... exactly the same thing, but o much more confusing when you don't really realise what's happening to/with that extra equation - this made it crystal clear :)
Thank you im in 8th grade and learning algebra my teacher doesn't explain it like you do.
Thanks for making the concept clear! You're a great teacher..
I'm looking at the comments in a bunch of videos and all these people seem like they are in a higher grade than me doing what I'm doing. I'm in 8th grade? What? I'm home schooled but someone pls answer my question. Why is this happening to me. Okay I'm done (btw u r better than my teacher)
The actual process is divide all terms by the coefficient of the x^2 before proceeding to the process explained.
Można także to równanie kwadratowe rozwiązać przy pomocy delty .
where was youtube when i was in highschool in the 80s
This really IS the best explanation!!
watched so many videos, this is the one that made me finally get it so thank you!
u are definitely surely amazingly better than my prof hat on you
lol my teacher explained the exact same thing but i only understood this one for some reason xD. Thanks this was helpful.
We could further simplify it as
-5 ± sqrt16 × sqrt2
-5 ± 4sqrt2
Doesnt radical 32 simplify in 4radical2
Yes.
That is the best explanation I have seen. Thanks.
Why does 1/2 of the coefficient of x suddenly come into the equation? What role does it play in it?
Is that right answer ? Can 32 square root become 16*2
Im from the Philippines
Good explanation bro
Great vid man, really helped me out can you do more?
Someone else needs a math channel called "In plane english"
This was Extremely helpful! thanks a ton!
My mind just got a workout! Well explained.
if the coefficient of x is -10, will you still add +25 to both sides or will you will you apply -25 instead. i am refering to an equation that looks like this x^2-10x-7=0 ??? Thank you
Literally the best explanation
But what if it isn’t 10x say it’s 13x or 17x
Actually better than my prof😂😂
Awesome Explanation!!! Thank you so much 🙏
Best explanation ever♥️
For a demo, why didn't you start with x^2 + 10x - 11 = 0 ? That way, after completing the square, you get a perfect square on each side.
Acellus needs to hire you. My daughter is so frustrated with math. Im so frustrated with my attempts to help her. Would you be upset it i wrote/spoke with the school about you?
Title is accurate. Thumbs up
this was very helpful ^.^
Well done, clear process and clear easy to follow notes.
Leaving sqr32 in math tests is unacceptable in my country. Should be sqr 16*2 = 4 sqr2.
BTW.
This quadratic equation might be figured way easily:
1/ Delta = b^2 - 4ac = 128
2/ sqr 128 = 4 sqr8
3/ x1 = -5 - 2 sqr8
X2 = -5 + 2 sqr8
Eot
What does solving a quadratic equation have to do with the real word? How would we get to the point where something physical was described by a quadratic equation?
Robert Brandywine You can apply it to some physics problems which have to do with real world situations.
you sir, are a GOD
better than our math teacher
It make sense thanks for sharing your ideas.
sir, the square root of 32 can be simplified further, right?
Yes: sqrt(32)=sqrt(16*2)=sqrt(16)*sqrt(2)=4*sqrt(2). He probably left out the simplification so as not to distract from the main point of the video, but you make a good point.
He didn't work out the square root of 32 to avoid confusing the amateurs