Solve Using the Square Root Property 81x^2=25

$81 x^{2} = 25$

Step 1

Divide each term in $81 x^{2} = 25$ by $81$ and simplify.

Divide each term in $81 x^{2} = 25$ by $81$ .

$\frac{81 x^{2}}{81} = \frac{25}{81}$

Simplify the left side.

Cancel the common factor of $81$ .

Cancel the common factor.

$\frac{81 x^{2}}{81} = \frac{25}{81}$

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

$x^{2} = \frac{25}{81}$

Step 2

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

$x = \pm \sqrt{\frac{25}{81}}$

Step 3

Simplify $\pm \sqrt{\frac{25}{81}}$ .

Rewrite $\sqrt{\frac{25}{81}}$ as $\frac{\sqrt{25}}{\sqrt{81}}$ .

$x = \pm \frac{\sqrt{25}}{\sqrt{81}}$

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{\sqrt{5^{2}}}{\sqrt{81}}$

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

$x = \pm \frac{5}{\sqrt{81}}$

Simplify the denominator.

Rewrite $81$ as $9^{2}$ .

$x = \pm \frac{5}{\sqrt{9^{2}}}$

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

$x = \pm \frac{5}{9}$

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.

$x = \frac{5}{9}$

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

$x = - \frac{5}{9}$

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

$x = \frac{5}{9}, - \frac{5}{9}$