# How do you solve by completing the square for  2x^2 - 4x + 5 = 0?

Jun 3, 2015

$2 {x}^{2} - 4 x + 5 = 0$

$\textcolor{w h i t e}{\text{XXXX}}$$2 \left({x}^{2} - 2 x\right) = - 5$

$\textcolor{w h i t e}{\text{XXXX}}$$2 \left({x}^{2} - 2 x + 1\right) = - 5 + 2$

$\textcolor{w h i t e}{\text{XXXX}}$${\left(x - 1\right)}^{2} = - \frac{3}{2}$

$\textcolor{w h i t e}{\text{XXXX}}$$x - 1 = \pm \sqrt{- \frac{3}{2}}$

note: there will be no Real solutions
$\textcolor{w h i t e}{\text{XXXX}}$$x = 1 \pm \sqrt{\frac{3}{2}} i$