# How do you solve the equation 3x^2-150=-282?

Jun 2, 2017

No real solution

Complex solutions: $x = \pm 2 \sqrt{11} i$

#### Explanation:

Given: $3 {x}^{2} - 150 = - 282$

Start by adding $282$ to both sides of the equation: $3 {x}^{2} - 150 + 282 = 0$

$3 {x}^{2} + 132 = 0$

Factor the greatest common factor (GCF) of $3$:

$3 \left({x}^{2} + 44\right) = 0$

If you divide both sides by $3$ you get:

${x}^{2} + 44 = 0$

${x}^{2} = - 44$

When you square root both sides you will get a negative value which yields a complex solution since $\sqrt{- 1} = i$:

$x = \pm \sqrt{- 44} = \pm 2 \sqrt{- 11} = \pm 2 \sqrt{11} i$

No real solution.