Answer
$z=\pm 2i\sqrt{53}$
Work Step by Step
$-2z^{2}=424\qquad$ ...divide the entire expression with $-2$.
$ z^{2}=-212\qquad$ ...take square roots of each side.
$ z=\pm\sqrt{-212}\qquad$ ...simplify $\sqrt{-212}=i\sqrt{212}=i\sqrt{4\cdot 53}=2i\sqrt{53}$
$z=\pm 2i\sqrt{53}$
