# How do you solve  x^2 - 2x + 4 using the quadratic formula?

Jul 5, 2015

${x}^{2} - 2 x + 4 = 0$ has no real solutions, only complex ones, but the quadratic formula does work to give:

$x = 1 \pm i \sqrt{3}$

#### Explanation:

${x}^{2} - 2 x + 4$ is of the form $a {x}^{2} + b x + c$

with $a = 1$, $b = - 2$ and $c = 4$

The quadratic formula gives us the solutions to ${x}^{2} - 2 x + 4$ as:

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

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

$= \frac{2 \pm \sqrt{- 12}}{2}$

$= \frac{2 \pm 2 \sqrt{- 3}}{2}$

$= 1 \pm i \sqrt{3}$