Solve the Equation by Completing the Square $$\frac { x ^ { 2 } } { 2 } + \frac { 1 } { 2 } x = 8$$

Solve the equation by completing the square. Express any complex numbers using i notation.
- $$\frac { x ^ { 2 } } { 2 } + \frac { 1 } { 2 } x = 8$$

A) $\frac { - 1 \pm \sqrt { 65 } } { 4 }$
B) $\frac { 1 \pm \sqrt { 65 } } { 2 }$
C) $\frac { - 1 \pm \sqrt { 65 } } { 2 }$
D) $\frac { 1 \pm \sqrt { 65 } } { 4 }$