# How do you solve using the completing the square method x^2-20x=10?

Apr 6, 2018

$x = \pm \sqrt{110} - 10$

#### Explanation:

The first step required to complete the square is to have your constant on one side, and variables on the other, in the form

$a {x}^{2} + b x = c$. This is the case here.

Now, you must add ${\left(\frac{b}{2}\right)}^{2}$ to each side. Here, $b = - 20 , {\left(\frac{b}{2}\right)}^{2} = {\left(- \frac{20}{2}\right)}^{2} = 100$

Thus, we have

${x}^{2} - 20 x + 100 = 10 + 100$

${x}^{2} + 20 x + 100 = 110$

We need to factor the left side. Recognize that $\left({x}^{2} + 20 x + 100\right) = \left(x + 10\right) \left(x + 10\right) = {\left(x + 10\right)}^{2}$

${\left(x + 10\right)}^{2} = 110$

To solve, take the root of each side, accounting for positive and negative answers.

$\sqrt{{\left(x + 10\right)}^{2}} = \pm \sqrt{110}$

$x + 10 = \pm \sqrt{110}$

Solve.

$x = \pm \sqrt{110} - 10$