# How do you solve  x^2+3=0?

Jan 6, 2017

Put all the variables on one side of the equal sign, then solve from there.

#### Explanation:

You want to get all the variables over to one side, so subtract 3 over to the right side. You should then get ${x}^{2} = - 3$.

You'd then square root both sides to get the simplified version of x.

$\sqrt{{x}^{2}} = \sqrt{- 3}$

The square root of ${x}^{2}$ is simply x, but the $\sqrt{- 3}$ is more complicated, as you can't get the square root of a negative number. You'd have to involve $i$, or the idea of an imaginary number.

(Right now, we have $x = \sqrt{- 3}$

Because $i = \sqrt{- 1}$, we could multiply our 3 and $i$.
If $\sqrt{- 3} = 3 \cdot \sqrt{- 1} = 3 i$, then $x = 3 i$.