Solve Using the Square Root Property 5x^2=240

$5 x^{2} = 240$

Step 1

Divide each term in $5 x^{2} = 240$ by $5$ and simplify.

Divide each term in $5 x^{2} = 240$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{240}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{240}{5}$

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

$x^{2} = \frac{240}{5}$

Simplify the right side.

Divide $240$ by $5$ .

$x^{2} = 48$

Step 2

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

$x = \pm \sqrt{48}$

Step 3

Simplify $\pm \sqrt{48}$ .

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x = \pm \sqrt{16 (3)}$

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

$x = \pm \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm 4 \sqrt{3}$

Step 4

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.

$x = 4 \sqrt{3}$

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

$x = - 4 \sqrt{3}$

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

$x = 4 \sqrt{3}, - 4 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 4 \sqrt{3}, - 4 \sqrt{3}$

Decimal Form:

$x = 6.92820323 \dots, - 6.92820323 \dots$