# How do you complete the square to solve x^2 + 6x = -8?

Jun 3, 2015

Given ${x}^{2} + 6 x = - 8$

If ${x}^{2} + 6 x$ are the first two terms of a squared binomial of the form:
$\textcolor{w h i t e}{\text{XXXX}}$${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$
then
$\textcolor{w h i t e}{\text{XXXX}}$$a = 3$

${x}^{2} + 6 x + 9 = - 8 + 9$

${\left(x + 3\right)}^{2} = 1$

$x + 3 = \pm 1$

$x = - 2$ or $x = - 4$