Solve Using the Square Root Property 3x^2+4=13

$3 x^{2} + 4 = 13$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$3 x^{2} = 13 - 4$

Subtract $4$ from $13$ .

$3 x^{2} = 9$

Step 2

Divide each term in $3 x^{2} = 9$ by $3$ and simplify.

Divide each term in $3 x^{2} = 9$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{9}{3}$

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

$x^{2} = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x^{2} = 3$

Step 3

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

$x = \pm \sqrt{3}$

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.

$x = \sqrt{3}$

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

$x = - \sqrt{3}$

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$