Solve Using the Square Root Property 16x^2=9

$16 x^{2} = 9$

Step 1

Divide each term in $16 x^{2} = 9$ by $16$ and simplify.

Divide each term in $16 x^{2} = 9$ by $16$ .

$\frac{16 x^{2}}{16} = \frac{9}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x^{2}}{16} = \frac{9}{16}$

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

$x^{2} = \frac{9}{16}$

Step 2

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

$x = \pm \sqrt{\frac{9}{16}}$

Step 3

Simplify $\pm \sqrt{\frac{9}{16}}$ .

Rewrite $\sqrt{\frac{9}{16}}$ as $\frac{\sqrt{9}}{\sqrt{16}}$ .

$x = \pm \frac{\sqrt{9}}{\sqrt{16}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{3^{2}}}{\sqrt{16}}$

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

$x = \pm \frac{3}{\sqrt{16}}$

Simplify the denominator.

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

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

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

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

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.

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

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

$x = - \frac{3}{4}$

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

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