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

Mar 25, 2018

No solution

#### Explanation:

${\left(x + 2\right)}^{2} = - 7$
${x}^{2} + 4 x + 4 = - 7$
${x}^{2} + 4 x + 11 = 0$

Now I use the discriminant to determine if there is a solution

${b}^{2} - 4 a c$

${4}^{2} - \left(4.7\right)$
$16 - 28$

Already, discriminant is less than zero there there are no real solutions for x.

Mar 25, 2018

$x = - 2 \pm i \sqrt{7}$

#### Explanation:

There are many ways to tackle this; the easiest and quickest way here would be the square root method: take the square root of both sides:

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

$x + 2 = \pm \sqrt{- 7}$

Since you cannot take the square root of a negative and get a real number, there is no real solution to this equation. However, we can simplify to get a complex solution:

$x + 2 = \pm \sqrt{7} \cdot \sqrt{- 1}$

$x + 2 = \pm i \sqrt{7}$

$x = - 2 \pm i \sqrt{7}$