Solve Using the Square Root Property 4x^2-180=0

$4 x^{2} - 180 = 0$

Step 1

Add $180$ to both sides of the equation.

$4 x^{2} = 180$

Step 2

Divide each term in $4 x^{2} = 180$ by $4$ and simplify.

Divide each term in $4 x^{2} = 180$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{180}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{180}{4}$

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

$x^{2} = \frac{180}{4}$

Simplify the right side.

Divide $180$ by $4$ .

$x^{2} = 45$

Step 3

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

$x = \pm \sqrt{45}$

Step 4

Simplify $\pm \sqrt{45}$ .

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$x = \pm \sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$x = \pm 3 \sqrt{5}$

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.

$x = 3 \sqrt{5}$

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

$x = - 3 \sqrt{5}$

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

$x = 3 \sqrt{5}, - 3 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{5}, - 3 \sqrt{5}$

Decimal Form:

$x = 6.70820393 \dots, - 6.70820393 \dots$