Solve Using the Square Root Property 3x^2-45=0

$3 x^{2} - 45 = 0$

Step 1

Add $45$ to both sides of the equation.

$3 x^{2} = 45$

Step 2

Divide each term in $3 x^{2} = 45$ by $3$ and simplify.

Divide each term in $3 x^{2} = 45$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{45}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{45}{3}$

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

$x^{2} = \frac{45}{3}$

Simplify the right side.

Divide $45$ by $3$ .

$x^{2} = 15$

Step 3

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

$x = \pm \sqrt{15}$

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.

$x = \sqrt{15}$

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

$x = - \sqrt{15}$

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

$x = \sqrt{15}, - \sqrt{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{15}, - \sqrt{15}$

Decimal Form:

$x = 3.87298334 \dots, - 3.87298334 \dots$