# Solving Equations by Completing the Square

In this video, we are going to look at how to solve equations by completing the square.
For example:
If we are given
$x^2+4x-11=0$
we can try to factor it, but it would not work. This is when we would solve by completing the square. First we want to get rid of the last term, so we will add 11 to both sides, giving us
$x^2+4x=11$
Now we can complete the square.
$(\frac{b}{2})^2=(\frac{4}{2})^2=4$
Since we want to add 4 to the left side to complete the square, we must also add 4 to the right side to keep the equation the same. At this point we have
$x^2+4x+4=15$
Now if we factor it, we have
$(x+2)(x+2)=15$
Or it can also be written as
$(x+2)^2=15$
From here we take the square root of both sides
$\sqrt{(x+2)^2}=\sqrt{15}$
So
$x+2=\pm\sqrt{15}$
Solve for x by subtracting 2 and the final answer is
$x=-2\pm\sqrt{15}$

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