Solving by completing the square hard with fractions

👉 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 side 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.

Timestamp:
0:00 Intro
1:11 Start of Problem

Corrections:
5:40 Made a mistake in multiplying (49/16) with 2. (49/16) multiplied by 2 should have been (49/8).

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

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#Solvequadratics #completethesquare #brianmclogan

[zacrblx]

yes, he's human. yes, he made a small mistake. thanks for pointing it out guys, but some of you are plain rude! here he is helping you, providing education to all of you who are stuck doing an assignment at 12am, so at least appreciate it. i understand that it may have confused you, but he's honestly trying his best. thank you so much brian, you are extremely helpful. don't take the rude comments personally. one small mistake in the middle of the tons of help you've given to thousands of people is nothing, and all of these nasty commenters should realize that. sorry for sounding like a grouchy old lady complaining, but it's the truth. you are putting your full effort in to help us all, and i really really respect and appreciate that. :)

[CasaErwin]

This would have been so much less confusing if he had simply divided both sides by 2 in the first step.

[vedchabig]

Thank you sir, I am taking Calculus 3 in college but constantly find myself returning and having to relearn basic algebraic and trigonometric concepts. My memory my have failed me but you have not.

[alisontaylor]

i would like to say that you sir have helped me through some of the darkest hours- i would be no where without you.

[edwinmariano]

Always divide all terms by the coefficient of x squared first. This actually applies everytime when completing the square

[StingerVStang]

Love watching your videos. Make understanding math easier

[jamming]

please note:

@05:40 must be
98/16

the rest is wrong, after that one.
since the denominator has been multiplied @ 49/16 * 2

please correct me if I'm wrong. Thank You

[ajmiller]

Remember: the coefficient of X^2 has to be 1. It would have been less confusing to have met that criteria to begin with and then continue with completing the square, but everyone has their own way. (you pull into your driveway which is to the right of your front door. You want to enter your house through the front door. You get out of the car and have two choices: (1) walk left directly to the front door, or (2) walk around the back of the house and approach the front door. So which makes better sense even though there are two ways to get to the door?

[nehalkacholia]

THANKYOU!! I have a math test on Wednesday and my teacher's gonna give me completing the square with a greater than one and he didnt even bother teaching us how so Thankyouuu!!!!

[inxiti]

Here from KhanAcademy because they skipped a step.

Thank you for “this side is still is being multiplied by 2 so the other side needs to have its (49/16) multiplied by 2”!

Some of the answers felt magical, and random(when to, and when not to do an action.)

Thanks.

[TheFarmanimalfriend]

Brian Logan is making a straight forward process, complex and confusing.

[bigstuff]

was this an algebra 2 class?....what a wonderful time in my life 55 years ago...thank you for the video...

[honda.civiccalasiao]

The ans. is X= -4, X=1/2 or (X+4) (2X-1)

[anis]

Hey Brian,
Have you tried to multiply both sides by 4a and adding b^2 to both sides of the equation. This eliminates all possible fractions and in my opinion is actually easier than the quadratic formula.
2x^2+7x-4=0 (multiply both sides by 4a=4*2=8)
16x^2+56x-32=0(add b^2=7*7=49 to both sides.
16x*x+56x+49=49+32
(4x+7)^2 =81
4x+7=+/-9
4x=-7+/-9
X=(-7+/-9)/4
X=-4 or 1/2

[kurtshantalle]

Thank you hehe. That's our lesson in 3rd topic on Grade 9

[johnnolen]

Something went wrong somewhere.
2x^2 - 7x - 4 = 0 factors as (2x + 1)(x - 4) = 0. There's not a square root anywhere to be seen. (Hint: Before attempting CTS, divide each term by a.)

[quirkyqueen]

Thank you so much! Your videos are super helpful and help me to better understand my course material, which my teacher moves through at a rapid rate. Thanks again!

[lulezimaliaj]

Why did you not get rid of 2 on the step three by dividing everything by 2?

[apanaglima]

How did you get the -14 in your final answer

[peterpeggycheah]

Hi Mr Brian M.my methods for 2X square+7X—4=0 by Factorisation (2X+1)(X—4)=0 ; (2X+1)=0; 2X=—-1; X=—1/2 ;(X—4)=0 so X=4 Ans X= —1/2 or 4 .