Answer
$x=\pm 3i$
Work Step by Step
Isolating the squared variable and then taking the square root of both sides, the solutions of the given quadratic equation, $
2x^2+18=0
,$ are
\begin{array}{l}\require{cancel}
2x^2=-18
\\\\
x^2=-\dfrac{18}{2}
\\\\
x^2=-9
\\\\
x=\pm\sqrt{-9}
\\\\
x=\pm\sqrt{-1}\cdot\sqrt{9}
\\\\
x=\pm i\cdot\sqrt{(3)^2}
\\\\
x=\pm 3i
.\end{array}