Answer
$x=\dfrac{1}{2}\pm\dfrac{\sqrt{7}}{2}i$
Work Step by Step
$x^{2}-x+2=0$
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 $c=2$.
Substitute the known values in the formula:
$x=\dfrac{-(-1)\pm\sqrt{(-1)^{2}-4(1)(2)}}{2(1)}=\dfrac{1\pm\sqrt{1-8}}{2}=...$
$...=\dfrac{1\pm\sqrt{-7}}{2}=\dfrac{1}{2}\pm\dfrac{\sqrt{7}}{2}i$
The solution is $x=\dfrac{1}{2}\pm\dfrac{\sqrt{7}}{2}i$
