Answer
$x=-3\pm\sqrt{7}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
x^2+6x+2=0\\
x^2+6x=-2\\
x^2+6x+\left( \dfrac{6}{2} \right)^2=-2+\left(\dfrac{6}{2}\right)^2\\
x^2+6x+9=-2+9\\
(x+3)^2=7\\
x+3=\pm\sqrt{7}\\
x=-3\pm\sqrt{7}
.\end{array}
