Solve Using the Square Root Property 3x^2=81

$3 x^{2} = 81$

Step 1

Divide each term in $3 x^{2} = 81$ by $3$ and simplify.

Divide each term in $3 x^{2} = 81$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{81}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{81}{3}$

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

$x^{2} = \frac{81}{3}$

Simplify the right side.

Divide $81$ by $3$ .

$x^{2} = 27$

Step 2

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

$x = \pm \sqrt{27}$

Step 3

Simplify $\pm \sqrt{27}$ .

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$x = \pm \sqrt{9 (3)}$

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

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

Pull terms out from under the radical.

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

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.

$x = 3 \sqrt{3}$

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

$x = - 3 \sqrt{3}$

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

$x = 3 \sqrt{3}, - 3 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{3}, - 3 \sqrt{3}$

Decimal Form:

$x = 5.19615242 \dots, - 5.19615242 \dots$