How do you solve x^2 - 2x = 1 using completing the square?

Jun 19, 2015

I found:
${x}_{1} = 1 + \sqrt{2}$
${x}_{2} = 1 - \sqrt{2}$

Explanation:

Add and subtract $1$ to get:
${x}^{2} - 2 x \textcolor{red}{+ 1 - 1} = 1$
so:
${x}^{2} - 2 x \textcolor{red}{+ 1} = 1 \textcolor{red}{+ 1}$
${\left(x - 1\right)}^{2} = 2$
$x - 1 = \pm \sqrt{2}$
$x = 1 \pm \sqrt{2}$
${x}_{1} = 1 + \sqrt{2}$
${x}_{2} = 1 - \sqrt{2}$