Solving a quadratic by completing the square

👉 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.

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

[MFM]

I was impressed by the teacher, Mr. McLogan, who kept stopping to answer a question from a student. I bet he is a great teacher. Also, too many math teachers skip steps because the skipped step is "obvious." Of course, it it obvious to highly intelligent people with a gift for math. Mr. McLogan did all the steps. Very well done!

[nathanshell]

Not the hero we deserved, but the hero we needed.

This man is carrying me through my college courses.
Thank you Mr. Brian McLogan. I owe you bigtime!

[mikeoliver]

There are 3 methods:
1) factorise, if possible (by far the easiest, when possible).
If not 1), then
2) use the formula for roots of a quadratic equation (x = -b +/- etc)
3) complete the square, which is preferred when the coefficient of x is an even number.
{Completing the square in such a case also reveals the co-ordinates of the Vertex
eg with y = x^2 -4x -2, completing the square yields
y = (x -2)^2 - 6 which has a minimum value of -6 when x = 2.
The Vertex is the point (2, -6)}, which also reveals the Axis of symmetry ie the line x = 2.

A useful "test", so to speak, is to get students to work out the discriminant (b^2 - 4ac) which always tells the student a lot about the quadratic. Evaluating the discriminant is never a waste of time, because
--- it's good mental gymnastics ie brain exercise, with the additional caveat of the dangers of negative numbers, and
--- prepares the student for the type (and graph) of the quadratic they are dealing with.
eg when b^2 - 4ac = 0, there is only one real root, which means the quadratic itself is a perfect square. Useful for predicting solutions and sketching graphs.

In the case above, b^2 - 4ac = 81, which number is a perfect square.
When the discriminant is a perfect square, the quadratic has 2 real roots, which means that it can be factorised. ALWAYS.
2x^ + 7x -4 = 0
==> (2x - 1)(x + 4) = 0.
x = 1/2 and x = -4.

The question itself confuses me, so with respect:
Mr. McLogan, why would you get students to complete the square on
2x^2 + 7x -4 =0, unless it was specifically to teach/reinforce the technique of completing the square itself?
Completing the square on a Quadratic that can be factorised is unnecessarily complex and takes more time than factorising.
Flexibility is key and in Exams/Tests, a time-saver.

[adityamadiraja]

I got a 100% in 3 of my most important tests because of you! Thank you and keep making more videos like this!

[DimphoTsaModimo]

This video was recorded in 2012 but it still helped me a lot even in 2021 at varsity...Thank you so much, Sir. May God bless you.

[copkhan]

Math is the reason i became a Chef. Just cut, chop, cook and present. EASY.

[RhythmicSoundwaves]

In high school I decided not to pay attention in school, starting hanging around the wrong people and eventually after high school got my life in check and decided to go to college. I struggled so hard in math because of my HS situation. Your videos have helped so much. Today I can say I've graduated with a B.S in Exercise Science and on my way to getting a Doctorate.

[mathewthomas]

10 years later and this video still helps people like me - thank you for being a great teacher Mr.Logan

[johncrofford]

As someone who gets to explain this several times a year, I appreciate you taking the time to do this in front of a camera. Not sure why you didn't simplify that 2 out like you wanted to at the beginning, though. Simplifying as much as possible as early as possible cuts down on sloppy errors later.

[glennwadlegih]

I’ve been out of school for a very long time and have had a successful career in medical device engineering. I’ve honestly forgotten how good it was to have a great math teacher. I was fortunate to have quite a few of them and you are one of the good ones. When you are having a though day, remember you are making a difference!

[thembekilendlangamandla]

I wish I was part of the class being taught 😭😭❤

[daraung]

After finish giving a lecture on solving a quadratic equation.
Teacher: Any question?
Student raises hand.
Student: So a lot of it is algebra stuff.

[EmpyreanLightASMR]

College calc student here. You'll be doing this stuff all over again lmao here I am trying to refresh. Brings back memories of high school haha

[turtletube]

see this is why i really dislike math he filled up the whole board for one problem one freaking problem!!!!

[migelchavez]

Thanks you, you made me understand this material way better than my teacher .

[abokwu]

Quadratic formula seems far easier. ... for me at least... what is the purpose of using this method? Can't the Quadratic Formula just be used each time?

[utyouba]

Hi Brian. Many thanks for this ! Just one thing puzzled me ... when you had 2(x^2+7/2x)=4 why didn't you divide both sides by 2 to leave x^2+7/2x=2 ? This would give easier numbers to work with later on.

[dumbelldorkx]

Such an amazing instructor. for someone scared of fractions, professor mclogan made me understand it so easily

[DravenFNM]

bro overcomplicated it, took me 4 lines

[lionelgunathilake]

I saw this video unexpectedly and I was shocked. Those steps are really complicated. I
was taught by my teachers to follow very simple steps when I was in grade 8. The steps are given below.




2x2+7x-4=0

2x2+8x-x-4=0

2x(x+4)-1(x+4)=0

(x+4)(2x-1)=0

x+4=0 or 2x-1=0

x=-4 or x=1/2