# How do you solve -3x^2-9=0?

Mar 15, 2018

sqrt3*i

#### Explanation:

-3x^2-9=0 rArr -3x^2=9 rArr x^2=9/-3 rArr x^2=-3 rArr x= sqrt(-3) rArr x= sqrt(3*-1) rArr x= sqrt3*i [as sqrt-1=i]

Mar 15, 2018

$x = i \sqrt{3}$

#### Explanation:

We can start by adding $9$ to both sides to get

$- 3 {x}^{2} = 9$

Next, we can divide both sides by $- 3$ to get

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

We can take the square root of both sides. NOTE: We are taking the square root of a negative number, so we will have a complex solution.

$x = \sqrt{- 3}$

$\implies x = \textcolor{b l u e}{\sqrt{- 1}} \cdot \sqrt{3}$

$\implies x = \textcolor{b l u e}{i} \sqrt{3}$

NOTE: $\sqrt{- 1} = i$

Our final solution is

$x = i \sqrt{3}$