Answer
$-0.5 + 0.865j, \ or, \ -0.5 - 0.865j$
Work Step by Step
For the equation $x^2 +x+1= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=1, \quad b=1, \quad c=1
.$$
That is,
$$
x=\frac{-1\pm \sqrt{1-4}}{2(1) }=-0.5 + 0.865j, \ or, \ -0.5 - 0.865j
.$$
