Answer:[tex]\large\boxed{x=-4-i\sqrt6\ \vee\ x=-4+i\sqrt6}[/tex]Step-by-step explanation:[tex]-2x^2-16x-44=0\qquad\text{divide both sides by (-2)}\\\\x^2+8x+22=0\\\\\text{Use the quadratic formula of}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=8,\ c=22\\\\b^2-4ac=8^2-4(1)(22)=64-88=-24\\\\\sqrt{-24}=\sqrt{(4)(6)(-1)}=\sqrt4\cdot\sqrt6\cdot\sqrt{-1}=2\cdot\sqrt6\cdot i=2i\sqrt6\\\\x_1=\dfrac{-8-2i\sqrt6}{2(1)}=\dfrac{-8}{2}-\dfrac{2i\sqrt6}{2}=-4-i\sqrt6\\\\x_2=\dfrac{-8+2i\sqrt6}{2(1)}=\dfrac{-8}{2}+\dfrac{2i\sqrt6}{2}=-4+i\sqrt6[/tex]