Answer
$-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$
Work Step by Step
$x^{2}+x+1=0$
We use the quadratic formula ($a=1, b=1, c=1$):
$\displaystyle x=\frac{-(1)\pm\sqrt{(1)^{2}-4*1*1}}{2(1)}=\frac{-1\pm\sqrt{1-4}}{2}=\frac{-1\pm\sqrt{-3}}{2}=\frac{-1\pm \sqrt{3}i}{2}=-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$
