# How do you solve x^2+2x=9 by completing the square?

Mar 12, 2017

The solutions are $S = \left\{- 4.162 , 2.162\right\}$

#### Explanation:

Let's complete the square

${x}^{2} + 2 x = 9$

We add ${\left(\frac{2}{2}\right)}^{2}$ to both sides

${x}^{2} + 2 x + 1 = 9 + 1$

The $L H S$ is

$\left({a}^{2} + 2 a b + {b}^{2}\right) = {\left(a + b\right)}^{2}$

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

Taking square roots on both sides

$x + 1 = \pm \sqrt{10}$

$x = - 1 \pm \sqrt{10}$

${x}_{1} = - 1 - \sqrt{10} = - 4.162$

${x}_{2} = - 1 + \sqrt{10} = 2.162$