# How do you solve the equation x^2-2x-10=0 by completing the square?

Jun 6, 2017

$x = 1 \pm \sqrt{11}$

#### Explanation:

${x}^{2} - 2 x - 10 = 0$

half the coefficient of $x$ square it, add and subtract to the equation

$\left({x}^{2} - 2 x + {1}^{2}\right) - {1}^{2} - 10 = 0$

The bracket is a perfect square

$\implies {\left(x - 1\right)}^{2} - 11 = 0$

${\left(x - 1\right)}^{2} = 11$

$x - 1 = \pm \sqrt{11}$

$x = 1 \pm \sqrt{11}$