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

Mar 6, 2017

$x = 2 \pm i$

#### Explanation:

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

1) half the coefficient of $x$ square, add and subtract to balance

$\textcolor{b l u e}{{x}^{2} - 4 x + {2}^{2}} + 5 - {2}^{2} = 0$

$\text{2) the blue terms form a perfect square}$

$\textcolor{b l u e}{{\left(x - 2\right)}^{2}} + 5 - 4 = 0$

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

3) solve for $x$

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

$x - 2 = \pm \sqrt{- 1}$

$x - 2 = \pm i$

$\therefore x = 2 \pm i$