Answer
$x=-4-\sqrt{10}$ OR $x=-4+\sqrt{10}$
Work Step by Step
In the form $x^2+bx=c,$ the given equation, $
x^2+8x+6=0
,$ is equivalent to
\begin{align*}
x^2+8x&=-6
.\end{align*}
Adding $\left( \dfrac{b}{2} \right)^2$ on both sides to complete the square of the left side results to
\begin{align*}
x^2+8x+\left(\dfrac{8}{2} \right)^2&=-6+\left(\dfrac{8}{2} \right)^2
\\\\
x^2+8x+\left(4 \right)^2&=-6+\left(4 \right)^2
\\
x^2+8x+16&=-6+16
\\
(x+4)^2&=10
.\end{align*}
Taking the square root of both sides (Square Root Property) and then solving for the variable, the equation above is equivalent to
\begin{align*}
x+4&=\pm\sqrt{10}
\\
x&=-4\pm\sqrt{10}
.\end{align*}
Hence, the solutions are
$x=-4-\sqrt{10}$ OR $x=-4+\sqrt{10}$.