# How do you solve x^2 + 6x + 2 = 0 by completing the square?

Apr 1, 2015

For information on why completing the square works click the blue link.

${x}^{2} + 6 x + 2 = 0$

$\left({x}^{2} + 6 x \textcolor{w h i t e}{\text{ssssssss}}\right) + 2 = 0$

$\frac{1}{2} \cdot 6 = 3$. and ${3}^{2} = 9$ so we need to add $9$ to get a complete square:

$\left({x}^{2} + 6 x + 9 - 9\right) + 2 = 0$

$\left({x}^{2} + 6 x + 9\right) - 9 + 2 = 0$

${\left(x + 3\right)}^{2} - 7 = 0$

${\left(x + 3\right)}^{2} = 7$

$x + 3 = \pm \sqrt{7}$

$x = - 3 \pm \sqrt{7}$

The solutions are: $- 3 - \sqrt{7}$, $- 3 + \sqrt{7}$