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

Jun 12, 2015

$x = 1 + i$

$x = 1 - i$

#### Explanation:

Make a perfect square trinomial by completing the square. A perfect square trinomial has the form of ${a}^{2} + 2 a b + {b}^{2} = {\left(a + b\right)}^{2}$ or ${a}^{2} - 2 a b + {b}^{2} = {\left(a - b\right)}^{2}$.

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

Subtract $2$ from both sides of the equation.

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

Divide the coefficient of the $x$ term by $2$ and square the result. Add it to both sides of the equation.

$\frac{- 2}{2} = - 1$; $- {1}^{2} = 1$

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

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

There is now a perfect square trinomial on the left side of the equation.

Factor the trinomial.

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

Take the square root of both sides and solve for $x$.

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

$x - 1 = \pm i$

$x = 1 \pm i$