Solve by completing the square | Step by Step Technique
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- čas přidán 3. 05. 2023
- This is step by step technique to solve the quadratic equation by completing the square methods.
It is very helpful for everyone especially who are learning this for the first time!
Definitely subscribing.. you're so clear ❤
I have never seen such a clear explanation of how to solve a kwadratic equation by completing the square.
This video should help many young people having problems with this topic .
Grtz from Amsterdam, the Netherlands.
its quadratic
LOL!
Thanks for this video. I would solve this easier 😅
WONDERFUL ! THANKS 👍
very logical and simple to understand..🙂💜
Thank you so much, I can now subscribe to this challenge, it surprised me how I understood how to complete the square technique in five minutes.
Excellent explanation. Very easy to understand although I’m still unsure of at least 1-2 parts of it. I must rewatch to learn…. Thank you ❤❤❤❤
Hi,
This is a great video of Completing the Square.
How do you video yourself working this problem with paper and pencil?
Thanks so much!
Happy New Year
Very very nice solving
THANKS for Solve Completing the Square Solution🥰🙏
Quadratic formula took less than 3 minutes to get answers.
But this question v ve to solve only by this method.
Unfortunately, exams may ask you to write polynomials in that specific form, which cannot be done with the formula. That would be wishful thinking.
Now the question requires you u to use the competing the square method then you have no choice but to comply
3x² + 4x - 15 = 0
Next, we have x² + 4x - 45 = 0
(x - 5)(x + 9) = 0
(x - 5/3)(x + 9/3) = 0
(3x - 5)(x + 3) = 0
Therefore, x + 3 = 0
x = -3
and,
3x - 5 = 0
3x = 5
x = 5/3
Ur good at mathes
bring back memories 😊
Thank you so much 😊
Thank you very much
Thanks ive learnt
3x^2 + 4x - 15 = 0
3x^2 + 9x - 5x - 15 = 0
3x (x + 3) - 5 (x + 3) = 0
(3x - 5) (x + 3) = 0
3x - 5 = 0 & x + 3 = 0
x = 5 / 3 & x = -3
🖕 Ma'am, is this process wrong?
This method is called product-sum rule.
In Video, there is another method shown by which you can also derive the solutions that is called completing the square. You can use different methods as and when required!
You speak fluent and beautiful English
Thank u jimmy 👍
How do we know we will add 1/2 both side
Why did we multiply 4/3 by 1/2? Are we allowed to do that without affecting the other side of equation?
Dividing the middle term by 2 (and squaring it) is part of Completing The Square. Dividing something by 2 and multiplying something by 1/2 are equivalent operations. As such, most people just multiply by 1/2 because it's faster (something they can do in their heads).
@@chocolateangel8743 Thank you! It has been too long for me, and tbh, I don’t even remember learning that method, only the other one mentioned in the comments. Thank you for showing me a new way to find the answer to this tricky problem.
@@JosieCat3 You're welcome. I was forced to re-discover math in order to help my niece and nephew with their homework, so I've learned a lot -- especially since they changed over to Common Core math. I was taught under the old-teaching model of algorithmic memorization, which basically was like, "You have two days to memorize this process (by doing lots of problems)." If we didn't get it, we were just screwed. 🤣
@@chocolateangel8743 I appreciate these problems so much more now that I am older…they just seem like interesting puzzles that I must know the answer to now! Your niece and nephew are lucky to have you and know that you care about their education. Nothing could be of more importance in these times than education that includes math and critical thinking skills.
@@JosieCat3 Yeah, math is more fun than teachers make it out to be. The only reason I got involved in their education is because my sister came in one day, threw some papers at me, and said, "If you don't figure this out, your niece and nephew are going to fail!" 🤣 We are only one year apart, so we grew up being taught the same way and basically had the same teachers. Besides wanting to help them, I was also curious as to whether or not the more conceptual approach would work better for me that the traditional one did.
I quickly learned that, when it comes to math, I'm more of a conceptual math learner. I'm the kind of person that needs to understand mathematical logic (concepts and properties, why something works the way it does) in order to successfully execute algorithms. I also tend to prefer alternative approaches to the standard algorithms. If you're having trouble with this standard approach, you might want to check out approaches that use area models or the Po-Shen Loh method, for example. Good luck!
When the second term is prime, i go to the quad. form . to try and avoid fractions. But you helped me face my fear with this video
Thanks a lot and keep it up ❤🇿🇲
Well understood ❤
The process which you said and our teacher is totally differnt but you explained nicely
well done thank you
I love it so much I will work hard
Thanks God bless you 🙏👌👌
Good logic 👍
Nice
YOU ARE THE BEST
where does 4/3x go.
thank s alot
This equation 3x² + 4x - 15 = 0 can be factored perfectly in (3x-5)(x+3)=0 so I will not complete the square.
Also the abc-formula is much easier and more insightful:
D = b² -4ac = (4)² - 4.(3).(-15) = 16 + 180 = 196 ( positive so 2 solutions for y = f(x) = 0 )
x-coordinate of top of parabola: xtop = -b/2a = -(4) / (2.3) = - 2/3
distance between xtop and x1,x2 : delta = SQR(D) / 2a = SQR(196) / (2.3) = 14 / 6 = 7/3
x = xtop MINUS/PLUS delta
x1 = - 2/3 MINUS 7/3 = -9/3 = - 3
x2 = - 2/3 PLUS 7/3 = 5/3
When I took Algebra in high school our math teacher spent only one day showing this and the next day, she showed how the quadratic formula came from this method and after that we just used the formula to solve equations.
It is much easier using the quadratic formula than going through the completed the square method.
but when you study higher algebra it is very useful method like in calculus
In college, I took three semesters of calculus and a course called advance math for engineering's. I do not remember doing completing the square in those classes. @@adityapingle4923
This is how the quadratic formula was found. Replace the numbers with a, b and c and use this same method and you will find it yourself.
@@AngryEgg6942 I believe I said that. The quadratic formula came from completed the square. Once you have the formula no is no need to go through the completing the square method.
Yes I agree @@jerrypaquette5470
bro i dont understand .. like do we always need to take the half of the middle number
A useful lesson. Completing the square can be cumbersome. This case lends itself to a much easier solution method.
Step One: Multiply the lead coefficient by the constant. 3 x -15 = -45
Step Two: Find factors of -45 that when added give us the coefficient of the second term: 9 and -5 are factors that add to 4.
Step Three: Divide the factors of 9 and -5 by the lead coefficient of 3: 9/3 and -5/3.
Step Four: Change the signs of 9/3 and -5/3 and simplify -9/3 for the answers of -3 and 5/3.
Yes this is better
Am watching this while I've a test tomorrow 😭😭
Fair enough, but simple factoring the trinomial is easier.
Except the question asked to solve by completing the square...
4/3 not equals to (2/3) power 2
Fun fact: this is how the quadratic formula was found. Also means there is no need for this way to solve anything and just use the quadratic formula.
Can you do checking?
If there is no x on right side of equation, there is an extraneous solution.
Very complicated method😮
Just had an assignment to solve this type of problem by factoring, quadratic formula, and completing the square.. didnt even answer the problem by completing the square lol. Idk why but it bugs me😅
Good
আপনি কি Japanese
What is this💀
4/6 not equal (2/3)**2
I thought it is (b/2)^2?
madam do you know 4 aur 2 cut jate hai multiply karne ke need nhi h lol!
🔥
Ans.-3
There is a quicker method that circumvents fractions: Multiply the equation with 12 (that's 4a) and THEN complete the square: (6x+4)^2=......and then take square roots. Done
0:17 did u hear what i heard?
Add fractions
4/6 = (2/3) exp2 😮 ?????
No the question is asking you to do from completing square method
❤
😮so confusing😢
See my post. There's an easier solution.
With nonmonic quadratic equations, you can avoid the use of fractions until the very last step by using Sridhara's method, which starts by multiplying both sides of the equation by four times the coefficient of the quadratic term and then complete the square by adding and subtracting the square of the coefficient of the linear term of the _original_ equation.
Using this method we can solve the equation in the video as follows:
3x² + 4x − 15 = 0
36x² + 48x − 180 = 0
36x² + 48x + 16 − 16 − 180 = 0
(6x + 4)² − 16 − 180 = 0
(6x + 4)² = 196
6x + 4 = 14 ⋁ 6x + 4 = −14
6x = 10 ⋁ 6x = −18
x = 5/3 ⋁ x = −3
With some practice, you can of course skip the third and next to last steps. Alternatively, we can start by bringing the constant term over to the right hand side as you do in the video, then we get
3x² + 4x = 15
36x² + 48x = 180
36x² + 48x + 16 = 196
(6x + 4)² = 196
6x + 4 = 14 ⋁ 6x + 4 = −14
x = 5/3 ⋁ x = −3
ap qustan pakistan ke smja rahi ho aur bat english me kar rahi ho wah
7th STD maths
This is all too complicated to remember… quadratic formula is literally easier and makes more sense
But in higher class while doing integration u need this method😅
@@ManiAdhikari-dh1cc integration who with who
That's to much many explain less and slower
That's too much gymnastic just use the discriminant equation and problem solve
My teacher wants us to use all equations. I'm only gonna use this for my math class
You can't just use that when the question specifically request you to use a particular method like this.
czcams.com/video/q7M-TlRioPo/video.htmlsi=jKPr_mXDKgHmph9e
czcams.com/video/q7M-TlRioPo/video.htmlsi=jKPr_mXDKgHmph9e
@Brocambro no one cares abt ur opinion
What happened to the 3 that was equal to both side, that was under 5 on the right side 🧐
I agree that’s not right
Kia ki ja rahi Hy ap
Took too long to solve this equation with unnecessary steps.
Lol cut cut
But why are you copying pre math CZcams channel?
You used too long and a complicated method. This equation should be solved in your brain without this lengthy process by selecting sum/product numbers.
(3X-5) & (X+3) = 0
X = 5/3 or X = -3
nega fifteen
Guys anyone who can help me how to solve the discount rate
Bkkk
😡
This is too much
You are wrong mom, this equation must not divided by three, in this case your knowledge in completing square of quadratic equation is lacking and too narrow, you must studying again about quadratic equation integrally.
Noo madam did it excellently n she is very very correct❤
@@emilymoigenyanchera1908 i mean, when you taking completing square method, you must not divided that equation by three, you can modify by root of three
What is wrong with the division of 3?
@@Visionaryminute it is seem that you are never understand about quadratic equation
Not wrong it's correct
not so good
Every time you see a fraction...bad bad bad. A fraction and a radical...asking for truble. Way better like @jim2376 does.
See my main comment on this video on how to solve this equation easily by completing the square, no fractions and no radicals.
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