# How do you solve using the completing the square method x^2 - 2x = 0?

Apr 3, 2017

$x = 0 \text{ or } x = 2$

#### Explanation:

To $\textcolor{b l u e}{\text{complete the square }}$on the left side of the equation.

• " add " (1/2 "coefficient of the x term")^2 to both sides.

$\text{That is } {\left(\frac{- 2}{2}\right)}^{2} = 1$

$\Rightarrow {x}^{2} - 2 x \textcolor{red}{+ 1} = 0 \textcolor{red}{+ 1}$

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

$\text{Take " color(blue)"the square root of both sides}$

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

$\Rightarrow x - 1 = \pm 1$

$\Rightarrow x = + 1 + 1 = 2 \leftarrow \textcolor{red}{\text{first solution" " or}}$

$x = - 1 + 1 = 0 \leftarrow \textcolor{red}{\text{ second solution}}$