Solve the Equation by Completing the Square $$x ^ { 2 } + x + 1 = 0$$

Multiple Choice

Solve the equation by completing the square.
- $$x ^ { 2 } + x + 1 = 0$$

A) $\left\{ \frac { - 1 \pm i \sqrt { 3 } } { 2 } \right\}$
B) $\left\{ \frac { - 1 \pm \sqrt { 3 } } { 2 } \right\}$
C) $\left\{ \frac { 1 \pm \sqrt { 3 } } { 2 } \right\}$
D) $\left\{ \frac { 1 \pm \mathrm { i } \sqrt { 3 } } { 2 } \right\}$