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Solving quadratic equations by completing the square | Algebra II | Khan Academy
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- čas přidán 11. 04. 2010
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Solving Quadratic Equations by Completing the Square
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
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Why can't we just listen to these guys videos in Math Class? In just 14 minutes, he taught me as much as two algebra teachers taught me in (no joke) six hours!
Math Teacher Logic
*Gets help on confusing topic* C'MON GUYS WHY DON'T YOU PAY ATTENTION I TAUGHT THIS IT EASY!!!
"any questions" says the math teacher. *silence* CMON WHY IS NOBODY ASKING QUESTION THIS IS HARD STUFF
+Misha Bjerken I take all my classes normally but I take math online. I can't understand any of my public schools math teachers so it's just a waste of time. I wish online school was how everyone was taught, it honestly saves so much time, because you can go at your pace.
Because then they will be boring because they will be more forced and concentration will be impossible because everyone else is talking over. The teachers are bad teachers, but the class is usually a bad class or at least in my experience.
@@BlackHatChannel really true Sal proves every formula and explains a lot better than all other teachers
You're 20 now. What's the state. How are you doing. What's going on.
this helped a lot more than my Algebra teacher
Same.
Ever since the 9th grade this channel has been getting me through my math subject. Bless this man 😩 thank you so much haha
If there was only one in biology I wouldn't be in borderline D
+Penguin YES This video pretty much saved my sixth grade gpa
@@amon7816 Khan Academy also covers Biology concepts as well!!
Me in 7th grade= This is easy!
Me in 9th grade= What is this witchcraft?
Me after watching this video= This is easy!
Sup shaurya. This is vishnu from nps yelahanka. If u remember.
@@rain7870 what's creepy??
this man is single-handedly carrying me through sophomore year
same dude my math teacher like speedruns our lessons 😭
Khan Academy: Helping kids with shitty teachers since 2006
@FredTheBread well then this comment is not for you...
I'm so glad things like this exist. Having been thrown into a room with someone who's a sorry excuse for a teacher teach you makes this stuff impossible.
I am in 9th grade and you sir just saved my life.
+KhalidHamid50 yo me too
Me too. Lol
saaaaame
I learned this in 7th grade
Pixeled Opper Yeah, you don't need to be a punk about it. Go brag somewhere else.
My teacher played a buffering old video in class that no one understood so I went to khan academy like always, teaching me more than my teachers since day 1
Dan Ab are you physically an advertisement?
Akira Douglas maybe
Thanks for picking up on my math teacher's slack. 💗
Honestly same
Mikaela Kozechik same
Thank you so much! My Algebra 2 teacher is Romanian and English is literally her fourth language. As you could imagine, she isn't the greatest teacher on the planet. I really appreciate it!
My brain just turned into a gelatinous pile of mush.
Congratulations.
10 years life and you sir are still saving 9th graders lives. 😂😂😂
we should have a holiday for you
Can you replace my math teacher please? I finally understand this! It's like I've learned the secrets to the universe! Is this how people who understand and enjoy math feel 24/7?!
WHY DA HELL IS MY TEACHER TELLING ME I NEED TO MASTER THIS WHEN I AM IN ALGEBRA 1?!?!.
because this will be so much useful in calculus
Do people appreciate the genius of this method, and how everything just works out?
Sal Khan is such a life saver. Literally helps me with everything, history, science and Maths. I have no problems with English.
YT - Rhianna A colon, (:), should have come after 'everything'. You're welcome.
Nationale Sozialistiche Deutsche Arbeiterpartei *leans into mic* wrong
thank you khan academy!! my girlfriend and i couldn’t cook pizza and we couldn’t complete the square either!! BUT YOU HELPED US SOLVE ONE OF THOSE PROBLEMS :))
I wish we just watched your video during math hour. Much easier to understand
I have ADHD and yet still I've learned more from these guys in this video than I have in algebra class throughout the whole unit on quadratic equations
Thank Khan Academy, what took my teacher 2 hours to explain and to get our class to understand; only took 5 minutes with this video. Now that is an accomplishment.
Thank you so much for this video, I was having lots of trouble with this process, but now it has cleared my mind!! Thanks again!!👏🏽👌🏽⚡️🔥😇
This man can teach me all these things in 15 mins than my teachers could in a few hours.
Honestly my teacher is fine...I just didn’t pay attention.
khan academy is one of the best things ive encountered in my life
You're good keep it up :D I didn't understand everything at the start but I got it towards the end Thank you very much you superior human being
bless this channel
Khan academy has saved me so many times now
Thank you sir. This was our second math lesson in 9th grade and you made me understand it more!! Thanks :D
khan u are tge BEST of all
Crazy that this has been helping people for 15 years
this was a lifesaver and I have a test in 15 min 😭
How’d it go
Did you pass?
They passed away
im jn algebra 1 in seventh grade and lemme just say THANK YOU SO MUCH
I hate quadratics
Where does the +/- come from @4:10? Many thanks
Arun Prathapan the number can be either positive or negative because a negative number times by itself is a positive. Eg: -3 squared equals 3 squared, therefore a square root can be a positive or negative
Love it when my math teacher doesn’t teach us how to do this and gives us a test today !!!
The only reason I still like math my teachers are o useless ily Khan academy
OMG did u know? all the modules and reference books didnt have this method here. however i thought that completing the square was difficult but i found ur method to be easy. so i used it and wala i got it right! im so happy cuz sincd last year whenever theres a question on completing the square ive been skipping it. thnk u
youre the besttttttttttttttttttttttt thankssssssssssssss
youre my online math teacherrrr.
Seriously, Sal, I **love** your work! Thank you.
I hate math, why do i have to study it WHY
shaikhah - My Friend, mathematics is completely logical, you just have to know how to solve the equations. As to why you have to study it, you’ll find out in a few more years.
Yeah i hate math too but math is everywhere so we need to study more about it
You save me. Thank you
10:27 And this is the moment when it all made sense. I had the question in my head why divide -3x by 2 if you're trying to make it a perfect square wouldn't you just square it? but no, you did it because now you're able to factor. And when you have (x-3/2)^2, -3/2x + -3/2x adds to get -3 because essentially what you've done is you got rid of the division by multiplying it by 2. But then (-3/2)^2 also multiplies to get you 9/4 which you have added to both sides so the equation is preserved
one of the few of your videos where I come out more confused than how I came in
THANK YOU!!!! This helped me study for my test
Btw I got a 100 on that test
@@helixshark1753 6 years later but congrats on 100 :D
This helps alot. I have to do this in online school and the slideshow explanation crap they give us just doesn't make sense. Dziękuję, Khan Academy.
Dear Math,
I am not a therapist, so solve your own problems.
Math test tomorrow on this stuff... I may as well not even show up... Too hard
the 2nd one was confusing but I can get this down easily even trigonometry isn't that hard to me, i just need to pass this placement test by next week.
I just finished algebra 1 and I'm moving on to geometry, my teacher gave us a packet for math to do over the summer and I don't think they ever taught us this.
I watch other videos and it makes sense, but I feel like I need to watch a Khan academy video multiple times and even then I don't get it. Wondering what the mental block is...
Completing the square is too difficult.
why dont you have ads on your videos??!! you would be making bank! and possibly having this as your carreer!!
lol this is his career, he aims to provide this service for us free of charge, because learning should be free. Search "Khan Academy Ted Talks" on CZcams to find out more about him, his organisation and their objectives
Well i mean it is still free to us even if he did put ads on
After watching sal’s video iam understanding math for the first time ever He’s great!!!!!!!!!!
THANK YOU MR KHAN. YOUDAMAN!
Omg u just made this topic so easy for me
Great explanation, studying for Algebra II finals... How did you get that ti 85 calculator on the computer?
You didn't hear this from me, but you can download Wabbitemu for either Windows or Android (I have it on both myself). Then you need a rom. google TI 85 rom, and the very first link is your friend. It should be to emuparadise. Download the zip, unzip it, and run wabbitemu and select the .bin file of version 10.0 (ti85v100.bin). On Android you need to rename the .bin file to .rom or wabbitemu won't find anything when you try to load your own rom when you start the app. Have fun!
So glad Khan Academy can step in a help with homework!
If needing to use khan academy makes you dumb then I’m proud to be dumb
11:18 Wait...WHAT?!? Did you click a button & get the Graphing Calculator?!? I would like to know how you did that please!
I did not understand at all
not this vid
Dividing fractions, as easy as pie,
Flip the second fraction, then multiply.
And don't forget to simplify,
Before it's time to say goodbye
brenda whitman Ita because he doesn't explain it well. if I had not known how to do this before watching this video, I would be confused as well.
He explained it just fine, it's just hard for the mentally challenged to understand.
ZATIONS wow.
2:50 is it 2ax = - 4x or - 2ax = - 4x ?
Hey really help with stuff that I am struggling with
he
thank you sal for everything you do. i came across your videos some point in elementary school because we had khan academy and now im in 12th grade! the videos my algebra teacher gave me are horrible so i decided to watch yours instead lol
this man, in 4 minutes, taught me what a private education failed to in 4 years.
Wow! Very well explained! Thanks!
its 2022 n this is still useful
If some of you were confused about why he separated the x-2 and x-2- remember that you have to find two numbers that add to give you b but multiply to give you c.
I think you used negative sign here ; (x-a)square . So isn't it that a=2 not -2 ?
I think he shld use (x+a)square in that case. So that a can be equal to -2
The seemingly ridiculous fractions (some in 3 figures or more), I find amusing. But it all works out in the end, because it is a perfect square. My professor said to leave them in fractional form, this is the more accurate answer.
the 10x^2 - 30x - 8 = 0 example saved my life
I really enjoyed your workout but I have some note on some parts sir from where you're using
x² -4x +? = (x - a)²
(x-a)² = x² - 2ax + a²
So by comparing both sides of the equation, we supposed to have
-2ax= -4x (not 2ax = -4x)
Therefore a = 2 (not -2)
But from the video, you got x = -2 and if you substitute it to the parentheses
(x - a)², it will now be [x - (-2)]² which will be (x+2)²
Hope you understand sir?
better and more polite than my teacher
DA Boss you are going to help me pass math!!!!!!!!! im trying not to hate it right now
You can also use (b÷2)^2 for the missing number
Thank you for sharing this video, made me understand the concept better.
can you help me to solve 10m^2x^2=40n^2p^6 using quadratic equation by extracting the square roots.....give me a complete solution please
No thanks
No thanks
thank you very much sir, you are the hope raiser for me to make me believe that I can do math😄😄
at 5:20 why did (x-5)(x+1) get become x=5 and x=-1 and not x=-5 and x=1 like in the problem?
cause either (x-5) or (x+1) has to equal to zero as (x-5)(x+1) = 0. Meaning that whatever you put in x, the expression has to equal zero.
I'm at 1st year college right now lmao
khan academy came in clutch
Y=x^2 +7x-5 can be written in the form (x+a)^2+b. What is the value of a and b???
I’ll be honest, I did not understand a thing. This is the only vid I couldn’t understand 😭
explained it waaay better than my 8th grade algebra teacher
This says algebra 2 . So I've been taking algebra 2 things in 8th grade... wow I'm so mad rn
your better than my teacher
u r actually a hero
You've done it Again mr. Khan 🐸
Thanks a lot Khan Academy
so would the condensed square be (x +a)^2?
I was absent when my teacher taught this ToT
it came bk to me during quarantine
4:38 is an alternative faster way to do the problem guys
Missed the lesson on this & reading the textbook doesn't help. Thank you (:
You're a life saver man!
That’s nifty.
Half a million views and only 500 likes...
+john greene Thats because most people watch it on the Khan Academy website itself
+razlight789 Yeah. I usually go on the website, but when I watch on my iPad, I go on YT because the Khan Academy app keeps crashing.
exuse me we can use b^2_(4.a.c) it is easy and time between 5 and 20second
Hello, and thank you in advance if anybody responds. And peace to all. I am taking a union apprenticeship test tomorrow basis of which is basic algebra, and geometry. i.e. linear distance from fraction to decimal and vice versa. Add/Subtraction unlike terms. Factoring Quad equations and solving quad.following a given formula.
As far as the geometry its radius, circumference, arc Lengths, parallel lines and transversals. Math was once effortless for me as i see it now in my girls 18,11,6.. Ya i know pray for me.. haha.
ATTENTION EVERYONE WATCHING AND CONFUSED: go watch patrick jmt vids they're much more comprehendible
why is a= -2 in first example, that would make x^2 - 2*-2 which would equate to +4 so then the equation becomes x^2 + 4x
I think he shld use (x+a)square int his case