# How do you solve x^2 + 4x = 7 by completing the square?

Feb 27, 2017

$x = \pm \sqrt{11} - 2$

#### Explanation:

${x}^{2} + 4 x = 7$; Add $4$ to both sides,

${x}^{2} + 4 x + 4 = 11$; now the LHS is a perfect square

$\left(x + 2\right) \left(x + 2\right) = 11$

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

Take the square root of both sides........

$x + 2 = \pm \sqrt{11}$

$x = \pm \sqrt{11} - 2$