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Completing the Square

In this video, we are going to look at how to complete the square.
For example:
If we are given
(x+3)^2
we can multiply it out to get
x^2+6x+9

Here we have
x^2+4x+c
and we want c to be some number so that when factored, both binomials are exactly the same. To figure out what this c value will be, we will do the following:
(\frac{b}{2})^2
So in this case,
(\frac{4}{2})^2 is the same as
2^2 or 4
In this case, c needs to be 4.

If we had something like
x^2+3x+c
then
(\frac{3}{2})^2=\frac{9}{4}
so
x^2+3x+\frac{9}{4}
If we had to factor from here, then the two terms are whatever \frac{b}{2} was. When we factor this we get
(x+\frac{3}{2})(x+\frac{3}{2})