# How do you solve x^2-x+3=0 using the quadratic formula?

May 7, 2016

$x = \frac{1}{2} \pm \frac{\sqrt{11}}{2} i$

#### Explanation:

${x}^{2} - x + 3 = 0$ is in the form $a {x}^{2} + b x + c = 0$ with $a = 1$, $b = - 1$ and $c = 3$.

This has roots given by the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$= \frac{1 \pm \sqrt{{\left(- 1\right)}^{2} - \left(4 \cdot 1 \cdot 3\right)}}{2 \cdot 1}$

$= \frac{1 \pm \sqrt{- 11}}{2}$

$= \frac{1 \pm \sqrt{11} i}{2}$

$= \frac{1}{2} \pm \frac{\sqrt{11}}{2} i$