# How do you solve x^2 + 8x = 7 by completing the square?

May 9, 2016

$x = - 4 \pm \sqrt{23}$

#### Explanation:

If we add $16$ to both sides then the left hand side of the equation becomes a perfect square:

${x}^{2} + 8 x + 16 = 23$

That is:

${\left(x + 4\right)}^{2} = 23$

So $x + 4$ is a square root of $23$.

It could be the positive or negative one:

$x + 4 = \pm \sqrt{23}$

Subtract $4$ from both sides to find:

$x = - 4 \pm \sqrt{23}$