Solve Using the Square Root Property 9x^2=81

$9 x^{2} = 81$

Step 1

Divide each term in $9 x^{2} = 81$ by $9$ and simplify.

Divide each term in $9 x^{2} = 81$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{81}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{81}{9}$

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

$x^{2} = \frac{81}{9}$

Simplify the right side.

Divide $81$ by $9$ .

$x^{2} = 9$

Step 2

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

$x = \pm \sqrt{9}$

Step 3

Simplify $\pm \sqrt{9}$ .

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

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

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

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$