Learn how to solve a quadratic by completing the square with fraction

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. If the coefficient of the quadratic term is not 1, we factor out the coefficient before creating the perfect square trinomial.

The perfect square trinomial is created by adding to both sides of the equation, the square of half the coefficient of the linear term (the term whose variable is not squared). Note that you must account for the factored out value when adding the square of half the linear term to the other side of the equation. Then the perfect square trinomial is evaluated and then we solve for the variable to get the solution(s) to the quadratic equation.

Timestamps:
0:00 Intro
0:40 Start of Problem

Corrections:
9:51 I made a mistake, -21/2 multiplied with 1/6 is -21/12. Final answer: -1/2 plus/minus \sqrt(21/12i)

Organized Videos:
✅How to Solve a Quadratic by Completing the Square
✅Solve a Quadratic by Completing the Square | Fractions
✅Solve a Quadratic by Completing the Square | -x^2+bx+c
✅Solve a Quadratic by Completing the Square | 2x^2+bx+c
✅Solve a Quadratic by Completing the Square | ax^2+bx+c
✅Solve a Quadratic by Completing the Square | x^2+bx+c
✅Solve a Quadratic by Completing the Square | Learn About

Connect with me:

#Solvequadratics #completethesquare #brianmclogan

[tylerlam]

hate to be a stickler on details, but (-21/2)(1/6) is (-21/12)

[chrissmith]

Thanks Brian, this made me look intelligent to my son when I showed him how to do it without the mistakes.

[kishalayamukherjee]

Instead of factoring out the coefficient, simply eliminate the coefficient by dividing both the sides by the coefficient to get the quadratic term as 1. In this example dividing both the sides of the equation by 6, we get: x^2 + x = -2. Then adding both sides by (1/2)^2 we get x^2+x+(1/2)^2 = -2+(1/2)^2. Next step: LHS (x+1/2)^2. It will be easier for the learners if you explain this transformation (from x^2+x+(1/2)^2 to (x+(1/2)^2 ) by citing the formula of a^2 +2ab+b^2 = (a+b)^2. Frequent using of the terms 'binominal' 'trinominal' will only create confusion among the beginners. RHS: -2+(1/2)^2 = -2+1/4= -7/4 [( 4*-2+1)/4=-7/4].

[dharam.]

There is mistake in your calculation and your answer to this quadraric equation is wrong.Do not teach them wrong

[wsysjek]

you know he is a great teacher when he explains to students why something matters!! also, most youtubers forget to explain that you must multiply b^2 when you add it to the right side, and thus I couldn´t be able to get to the result!! thank

[yokiyoki]

Thanks Brian Mclogan, this actually helped me with my maths homework :)

[lastchance]

wow, he sure can complicate a simple problem

[johnnolen]

Mr. McLogan,
The given solution to this problem is incorrect.
Starting from 6x^2 + 6x + 12 = 0. You can factor out a 6 and throw it away (the zero product property). That leaves x^2 + x + 2 = 0. You can then add & subtract 1/4 on the LHS: (x^2 + x + 1/4) + 2 - 1/4 = 0. Re-writing the entire expression: (x + 1/2)^2 + 7/4 = 0. Subtracting 7/4 from both sides: (x + 1/2)^2 = -7/4, which implies x = - 1/2 p/m i/2*sqrt(7).

[christopherellis]

Grown up students who cannot sit quietly and wait for what comes next, especially those who imagine that asking questions is a sign of intelligence.

[eddyvilla-wzzd]

Mr Logan, when I plug in the rectified result in the original equation does not check out. Am I doing something wrong?. Txxx

[chocolateangel]

Perhaps, you should consider learning the Po-Shen Loh method. It makes this problem really simple.

[jas]

Well even if there was a mistake, you taught the process well...besides the problem im trying to solve aint the same so the mistake wasnt a big deal

I just listened to how you did it

[hanskaminsky]

This is a overcomplicated method for solving a quadratic equation by completing the square, and also ending with an incorrect answer! The correct answer is: (-1 plus/minus i * sqr[7]) / 2

[pritamdhinsa]

Simple. Dividing by 6 gives X square+X +2=0. Complete square quadratic gives X square

[artmiller]

In class:
5+5=10

Homework:
734+555-432/69=12.42

Test:
With two sheep flying, one yellow and the other heading right, how much does a pound of asphalt cost, given that the cow is 10 years old?

[tumak]

Good morning! Divide both sides by the common factor FIRST!!
In this case divide by 6 and it's so much LESS WORK.
I would have picked a different example, with no common factor.
Cheers (Canadian mathematics teacher)

[iorguemaxwell]

-1/2 +/- i (sqr(7))/2, using the traditional and hated resolving formula...

[anishmathew]

*Ans wrong, do like this*
6(x^2+x) = -12
Cancel 6, we get x^2 +x = -2
x^ + x + 1/4 = -2+1/4 [adding square of 1/2 coifficient of x both side]

(x+1/2)^2 = -7/4
x+1/2 = i √7/2 or -i√7/2
So x = -1/2+i√7/2 or -1/2 -i√7/2
This is simple step

[mirajones]

Your channel is full of mistakes and difficult methods. I appreciate teachers on YouTube but why do you not correct the videos and add annotations. This is potentially harmful to a lot of people. Quality over quantity. You have way too many identical videos.

[eddyvilla-wzzd]

Mr Logan, at 9:55 you made an oversight. -21/2 × 1/6= -21/12. You wrote -21/36.