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

$25 x^{2} = 81$

Step 1

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

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

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

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

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

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

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

Step 2

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

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

Step 3

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

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

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

Simplify the numerator.

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

$x = \pm \frac{\sqrt{9^{2}}}{\sqrt{25}}$

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

$x = \pm \frac{9}{\sqrt{25}}$

Simplify the denominator.

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

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

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

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

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.

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

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

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

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

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