Answer
$x=\left\{ -4-i\sqrt{2},-4+i\sqrt{2} \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
y^2+8y+18=0
,$ is
\begin{array}{l}\require{cancel}
y^2+8y=-18
\\\\
y^2+8y+\left( \dfrac{8}{2} \right)^2=-18+\left( \dfrac{8}{2} \right)^2
\\\\
y^2+8y+16=-18+16
\\\\
(y+4)^2=-2
\\\\
y+4=\pm\sqrt{-2}
\\\\
y+4=\pm i\sqrt{2}
\\\\
y=-4\pm i\sqrt{2}
.\end{array}
Hence, $
x=\left\{ -4-i\sqrt{2},-4+i\sqrt{2} \right\}
.$