# How do you solve ( x + 7)^2 = -11?

Mar 22, 2017

$x = - 7 + i \sqrt{11} \mathmr{and} - 7 - i \sqrt{11}$

#### Explanation:

${\left(x + 7\right)}^{2} = - 11$

$\left(x + 7\right) = \pm \sqrt{- 11}$

$\left(x + 7\right) = \pm \sqrt{- 1 \cdot 11}$

$\left(x + 7\right) = \pm \sqrt{- 1} \cdot \sqrt{11}$

$\left(x + 7\right) = \pm i \cdot \sqrt{11}$, where ${i}^{2} = - 1$

$x = - 7 \pm i \sqrt{11}$

$x = - 7 + i \sqrt{11} \mathmr{and} - 7 - i \sqrt{11}$