QUADRATIC EQUATIONS : Completing The Square part.A (SPM, IGCSE, A-level...)

(Since my time is limited, so for every chapter I will skip some and only focus on parts which most of the students found problem with it. Maybe after I retire, then only I will complete those skipped parts.)

Today let's learn about CTS (Completing The Square).

At previous post,
I talked about Perfect Square Quadratic (PSQ),
since PSQ and CTS both relate to each other.

Why??

This is because before learning about CTS,

We need to be able to know what number should we fill in,
to make it become PSQ.

If you read my previous post,
you already know that the number is 16.

If you not yet read my previous post,
the link is here:
https://leonmathstuition.blogspot.com/2019/03/quadratic-equations-before-learning.html

Why 16??

It is very easy,
just take the -8x at the middle.

-8 divide by 2, get -4,
then square the -4, get 16.

After filling in 16, it became PSQ:

If you still don't really understand,
or you didn't read my previous post,
please don't be stubborn,
just read:
https://leonmathstuition.blogspot.com/2019/03/quadratic-equations-before-learning.html

Next,
let's practice some questions first.

For all the 10 questions below,
what number should we fill in to make it become PSQ:

Answer:

Okay,
let's start learning CTS now.

First let's have a look at an example question:

Answer:

We move the +3 to the other side of the equation,
then just do like the example above:

What number should we add to make it become PSQ?

Now we all know that the number is 16,
so:

Since it is an equation,
so when we +16 at the left hand side,
we need to +16 at the right hand side too.

For example: 2 + 3 = 5

If left hand side +4 : 2 + 3 + 4

Then will the right hand side still be 5??
OF COURSE NOT!

So both sides also +4.

2 + 3 + 4 = 5 + 4

Then only the left = right !

Let's get back to the example question.........

After +16,
the left hand side became PSQ,
then we can apply the Factorisation of PSQ that I mentioned in previous post:

Just like the square root of 9 can be +3 or -3,
so we need to consider that square root of 13 can be positive or negative too.

Of course,
you don't have to write until so troublesome when actually answering the question.

Let me show you the simplified version of answering:

One more example:

Answer:

That's all for now.

As usual,
10 questions to practice:

Answer:

We will go more in depth about CTS at next chapter.

Thank you!

End.

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Related articles:
Before learning Completing The Square


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