Solve Using the Square Root Property 3x^2+240=0

$3 x^{2} + 240 = 0$

Step 1

Subtract $240$ from both sides of the equation.

$3 x^{2} = - 240$

Step 2

Divide each term in $3 x^{2} = - 240$ by $3$ and simplify.

Divide each term in $3 x^{2} = - 240$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{- 240}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{- 240}{3}$

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

$x^{2} = \frac{- 240}{3}$

Simplify the right side.

Divide $- 240$ by $3$ .

$x^{2} = - 80$

Step 3

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

$x = \pm \sqrt{- 80}$

Step 4

Simplify $\pm \sqrt{- 80}$ .

Rewrite $- 80$ as $- 1 (80)$ .

$x = \pm \sqrt{- 1 (80)}$

Rewrite $\sqrt{- 1 (80)}$ as $\sqrt{- 1} \cdot \sqrt{80}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{80}$

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

$x = \pm i \cdot \sqrt{80}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$x = \pm i \cdot \sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$x = \pm i \cdot \sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$x = \pm i \cdot (4 \sqrt{5})$

Move $4$ to the left of $i$ .

$x = \pm 4 i \sqrt{5}$

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.

$x = 4 i \sqrt{5}$

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

$x = - 4 i \sqrt{5}$

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

$x = 4 i \sqrt{5}, - 4 i \sqrt{5}$