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

Aug 16, 2016

This quadratic has zeros $x = 1 \pm i$

#### Explanation:

${x}^{2} - 2 x + 2 = 0$

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

It has zeros given by the quadratic formula:

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

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

$= \frac{2 \pm \sqrt{4 - 8}}{2}$

$= \frac{2 \pm \sqrt{- 4}}{2}$

$= \frac{2 \pm \left(\sqrt{4}\right) i}{2}$

$= \frac{2 \pm 2 i}{2}$

$= 1 \pm i$