Solve Using the Square Root Property 3x^2+24=0

$3 x^{2} + 24 = 0$

Step 1

Subtract $24$ from both sides of the equation.

$3 x^{2} = - 24$

Step 2

Divide each term in $3 x^{2} = - 24$ by $3$ and simplify.

Divide each term in $3 x^{2} = - 24$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{- 24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{- 24}{3}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 24}{3}$

Simplify the right side.

Divide $- 24$ by $3$ .

$x^{2} = - 8$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 8}$

Step 4

Simplify $\pm \sqrt{- 8}$ .

Rewrite $- 8$ as $- 1 (8)$ .

$x = \pm \sqrt{- 1 (8)}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{8}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x = \pm i \cdot \sqrt{4 (2)}$

Rewrite $4$ as $2^{2}$ .

$x = \pm i \cdot \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm i \cdot (2 \sqrt{2})$

Move $2$ to the left of $i$ .

$x = \pm 2 i \sqrt{2}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 i \sqrt{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 i \sqrt{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2 i \sqrt{2}, - 2 i \sqrt{2}$