How do you solve 2x^2-2x+7=5 by completing the square?

Jul 19, 2017

$x = \frac{1 \pm i \sqrt{3}}{2}$

Explanation:

$2 {x}^{2} - 2 x = - 2$
${x}^{2} - x = - 1$
${x}^{2} - x + \frac{1}{4} = - 1 + \frac{1}{4}$
${\left(x - \frac{1}{2}\right)}^{2} = - \frac{3}{4} = \frac{3 {i}^{2}}{4}$
There are 2 complex roots:
$x - \frac{1}{2} = \pm \frac{i \sqrt{3}}{2}$
$x = \frac{1}{2} \pm \frac{i \sqrt{3}}{2} = \frac{1 \pm i \sqrt{3}}{2}$