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