# 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.

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