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

Apr 27, 2016

The solutions are:
color(green)(x = sqrt (-1) + 1  or,  color(green)(x = -sqrt (-1) + 1

#### Explanation:

${x}^{2} - 2 x + 2$

${x}^{2} - 2 x = - 2$

To write the Left Hand Side as a Perfect Square, we add 1 to both sides:

${x}^{2} - 2 x + 1 = - 2 + 1$

${x}^{2} - 2 \cdot 1 \cdot x + {1}^{2} = - 1$

Using the Identity color(blue)((a-b)^2 = a^2 - 2ab + b^2, we get

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

$x - 1 = \sqrt{- 1}$ or $x - 1 = - \sqrt{- 1}$

color(green)(x = sqrt (-1) + 1  or  color(green)(x = -sqrt (-1) + 1