Solve Using the Square Root Property 64x^2=9

$64 x^{2} = 9$

Step 1

Divide each term in $64 x^{2} = 9$ by $64$ and simplify.

Divide each term in $64 x^{2} = 9$ by $64$ .

$\frac{64 x^{2}}{64} = \frac{9}{64}$

Simplify the left side.

Cancel the common factor of $64$ .

Cancel the common factor.

$\frac{64 x^{2}}{64} = \frac{9}{64}$

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

$x^{2} = \frac{9}{64}$

Step 2

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

$x = \pm \sqrt{\frac{9}{64}}$

Step 3

Simplify $\pm \sqrt{\frac{9}{64}}$ .

Rewrite $\sqrt{\frac{9}{64}}$ as $\frac{\sqrt{9}}{\sqrt{64}}$ .

$x = \pm \frac{\sqrt{9}}{\sqrt{64}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{3^{2}}}{\sqrt{64}}$

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

$x = \pm \frac{3}{\sqrt{64}}$

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$x = \pm \frac{3}{\sqrt{8^{2}}}$

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

$x = \pm \frac{3}{8}$

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.

$x = \frac{3}{8}$

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

$x = - \frac{3}{8}$

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

$x = \frac{3}{8}, - \frac{3}{8}$