Answer
The solutions are $-4+\sqrt{10}$ and $-4-\sqrt{10}$.
Work Step by Step
$ 2k^{2}+16k=-12\qquad$ ...divide each side with 2
$ k^{2}+8k=-6\qquad$ ...square half the coefficient of $k$.
$(\displaystyle \frac{8}{2})^{2}=(4)^{2}=16\qquad$ ...add $16$ to each side of the expression
$ k^{2}+8k+16=-6+16\qquad$ ...simplify.
$ k^{2}+8k+16=10\qquad$ ... write left side as a binomial squared.
$(k+4)^{2}=10\qquad$ ...take square roots of each side.
$ k+4=\pm\sqrt{10}\qquad$ ...add $-4$ to each side.
$ k+4-4=\pm\sqrt{10}-4\qquad$ ...simplify.
$k=-4\pm\sqrt{10}$
