Solve Using the Square Root Property 3x^2-189=0

$3 x^{2} - 189 = 0$

Step 1

Add $189$ to both sides of the equation.

$3 x^{2} = 189$

Step 2

Divide each term in $3 x^{2} = 189$ by $3$ and simplify.

Divide each term in $3 x^{2} = 189$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{189}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{189}{3}$

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

$x^{2} = \frac{189}{3}$

Simplify the right side.

Divide $189$ by $3$ .

$x^{2} = 63$

Step 3

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

$x = \pm \sqrt{63}$

Step 4

Simplify $\pm \sqrt{63}$ .

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$x = \pm \sqrt{9 (7)}$

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

$x = \pm \sqrt{3^{2} \cdot 7}$

Pull terms out from under the radical.

$x = \pm 3 \sqrt{7}$

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.

$x = 3 \sqrt{7}$

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

$x = - 3 \sqrt{7}$

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

$x = 3 \sqrt{7}, - 3 \sqrt{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{7}, - 3 \sqrt{7}$

Decimal Form:

$x = 7.93725393 \dots, - 7.93725393 \dots$