Answer
$k = -0.683, -7.317$
Work Step by Step
$-2(k+4)^{2} + 8 = -14$
$-2[k(k+4)+4(k+4)] = -14 -8$
$-2[k^{2} +4k +4k + 16] = -22$
$-2[k^{2} +8k + 16] = -22$
$-2k^{2} - 16k - 32 = -22$
$-2k^{2} - 16k -32 + 22= 0$
$-2k^{2} - 16k -10= 0$
$-2(k^{2} + 8k + 5) = 0$
$k = \frac{-8±\sqrt {(8)^{2}-4(1)(5)}}{2(1)}$
$k = \frac{-8±\sqrt {64-4(1)(5)}}{2}$
$k = \frac{-8±\sqrt {64-20}}{2}$
$k = \frac{-8±2\sqrt {11}}{2}$
$k = \frac{-4±\sqrt {11}}{1}$
$k = -4±\sqrt {11}$
$k = -0.683, -7.317$
