# How do you complete the square to solve x^2 – 5x + 8=0?

May 22, 2015

Given ${x}^{2} - 5 x + 8 = 0$

Completing the square
${x}^{2} - 5 x + {\left(\frac{5}{2}\right)}^{2} + 8 - {\left(\frac{5}{2}\right)}^{2} = 0$

${\left(x - \frac{5}{2}\right)}^{2} = \frac{25}{4} - 8 = - \frac{7}{8}$

$x - \frac{5}{2} = \pm \sqrt{- \frac{7}{8}}$

Note: there are no Real roots

$x = \frac{5}{2} \pm \sqrt{\frac{7}{8}} i$