# How do you solve using the completing the square method x^2+ 8x + 2 = 0?

Apr 27, 2017

$x = - 4 \pm \sqrt{14}$

#### Explanation:

$\text{to use the method of "color(blue)"completing the square}$

add (1/2" coefficient of x-term")^2" to both sides"

$\text{that is add " (8/2)^2=16" to both sides}$

$\Rightarrow \left({x}^{2} + 8 x \textcolor{red}{+ 16}\right) + 2 = 0 \textcolor{red}{+ 16}$

$\Rightarrow {\left(x + 4\right)}^{2} + 2 = 16$

$\text{subtract 2 from both sides}$

${\left(x + 4\right)}^{2} \cancel{+ 2} \cancel{- 2} = 16 - 2$

$\Rightarrow {\left(x + 4\right)}^{2} = 14$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\sqrt{{\left(x + 4\right)}^{2}} = \pm \sqrt{14}$

$\Rightarrow x + 4 = \pm \sqrt{14}$

$\Rightarrow x = - 4 \pm \sqrt{14}$