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

Mar 20, 2016

Add $16$ to both sides to "complete the square" on the left hand side and hence find:

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

#### Explanation:

One way is as follows:

First add $16$ to both sides to get:

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

Note that ${x}^{2} + 8 x + 16 = {\left(x + 4\right)}^{2}$, so we have:

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

Therefore:

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

Hence:

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