# How do you solve x^2=6x-12?

Jun 28, 2016

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

#### Explanation:

let's rewrite the equation in the general form:

${x}^{2} - 6 x + 12 = 0$

and solve by the quadratic formula used when b is even and a=1

$x = \left(- \frac{b}{2} \pm \sqrt{{\left(\frac{b}{2}\right)}^{2} - c}\right)$

In this case a=1; b=-6; c=12, so

$x = 3 \pm \sqrt{9 - 12}$

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

no real solution, but complex