# How do you evaluate (8x - 2) ^ { 2} + 8= - 1?

Aug 13, 2017

See below.

#### Explanation:

${\left(8 x - 2\right)}^{2} + 8 = - 1$

${\left(8 x - 2\right)}^{2} = - 9$

If imaginary numbers are not accepted (assuming all real numbers), then there are no real solutions to this equation, as the square of a real number is always greater than or equal to zero (since $- 9$ is less than $0$, we cannot solve the equation).

If we accept imaginary numbers, then we continue as follows:

${\left(8 x - 2\right)}^{2} = - 9$

$8 x - 2 = \pm \sqrt{- 9} = \pm 3 i$

$8 x = \pm 3 i + 2$

$x = \frac{\pm 3 i + 2}{8}$