# What are the solutions to the equation x^2+2x+2=0?

Jul 5, 2017

$x = - 1 \pm i$

#### Explanation:

$\text{check the value of the "color(blue)"discriminant}$

$\text{with } a = 1 , b = 2 , c = 2$

$\Delta = {b}^{2} - 4 a c = 4 - 8 = - 4$

$\text{since " Delta<0" the equation has no real solutions}$

$\text{solve using the "color(blue)"quadratic formula}$

$x = \frac{- 2 \pm \sqrt{- 4}}{2} = \frac{- 2 \pm 2 i}{2}$

$\Rightarrow x = - 1 \pm i \text{ are the solutions}$