Solve Using the Square Root Property 4x^2-225=0

$4 x^{2} - 225 = 0$

Add $225$ to both sides of the equation.

$4 x^{2} = 225$

Divide each term in $4 x^{2} = 225$ by $4$ and simplify.

Divide each term in $4 x^{2} = 225$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{225}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{225}{4}$

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

$x^{2} = \frac{225}{4}$

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

$x = \pm \sqrt{\frac{225}{4}}$

Simplify $\pm \sqrt{\frac{225}{4}}$ .

Rewrite $\sqrt{\frac{225}{4}}$ as $\frac{\sqrt{225}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{225}}{\sqrt{4}}$

Simplify the numerator.

Rewrite $225$ as $15^{2}$ .

$x = \pm \frac{\sqrt{15^{2}}}{\sqrt{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{15}{\sqrt{4}}$

Simplify the denominator.

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

$x = \pm \frac{15}{\sqrt{2^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{15}{2}$

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.

$x = \frac{15}{2}$

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

$x = - \frac{15}{2}$

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

$x = \frac{15}{2}, - \frac{15}{2}$