# How do you solve using the completing the square method x^2 - 6x + 10 = 0?

Jan 31, 2017

$x = 3 \pm i$

#### Explanation:

${x}^{2} - 6 x + 10 = 0$

consider #coefficient of x, divide by 2

${\left(x - \frac{6}{2}\right)}^{2} - {\left(- \frac{6}{2}\right)}^{2} + 10 = 0$

${\left(x - 3\right)}^{2} - 9 + 10 = 0$

${\left(x - 3\right)}^{2} + 1 = 0$

${\left(x - 3\right)}^{2} = - 1$

${i}^{2} = - 1$, then $i = \pm \sqrt{- 1}$

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

$x = 3 \pm i$