Solve Using the Square Root Property 3x^2-243=0

$3 x^{2} - 243 = 0$

Step 1

Add $243$ to both sides of the equation.

$3 x^{2} = 243$

Step 2

Divide each term in $3 x^{2} = 243$ by $3$ and simplify.

Divide each term in $3 x^{2} = 243$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{243}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{243}{3}$

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

$x^{2} = \frac{243}{3}$

Simplify the right side.

Divide $243$ by $3$ .

$x^{2} = 81$

Step 3

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

$x = \pm \sqrt{81}$

Step 4

Simplify $\pm \sqrt{81}$ .

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

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

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

$x = \pm 9$

Step 5

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.

$x = 9$

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

$x = - 9$

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

$x = 9, - 9$