Answer
$x=-\dfrac{1}{2}\pm\dfrac{\sqrt{3}}{2}i$
Work Step by Step
$x^{2}+x+1=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=1$ and $c=1$.
Substitute the known values in the formula:
$x=\dfrac{-1\pm\sqrt{1^{2}-4(1)(1)}}{2(1)}=\dfrac{-1\pm\sqrt{1-4}}{2}=\dfrac{-1\pm\sqrt{-3}}{2}=...$
$...=\dfrac{-1\pm\sqrt{3}i}{2}=-\dfrac{1}{2}\pm\dfrac{\sqrt{3}}{2}i$
The answer is $x=-\dfrac{1}{2}\pm\dfrac{\sqrt{3}}{2}i$
