Solve Using the Square Root Property x^2=9/4

$x^{2} = \frac{9}{4}$

Step 1

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

$x = \pm \sqrt{\frac{9}{4}}$

Step 2

Simplify $\pm \sqrt{\frac{9}{4}}$ .

Rewrite $\sqrt{\frac{9}{4}}$ as $\frac{\sqrt{9}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{9}}{\sqrt{4}}$

Simplify the numerator.

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

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

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

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

Simplify the denominator.

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

$x = \pm \frac{3}{\sqrt{2^{2}}}$

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

$x = \pm \frac{3}{2}$

Step 3

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.

$x = \frac{3}{2}$

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

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

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

$x = \frac{3}{2}, - \frac{3}{2}$