Solve Using the Square Root Property 16-3x^2=13

$16 - 3 x^{2} = 13$

Step 1

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

Subtract $16$ from both sides of the equation.

$- 3 x^{2} = 13 - 16$

Subtract $16$ from $13$ .

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

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x^{2} = 1$

Step 3

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

$x = \pm \sqrt{1}$

Step 4

Any root of $1$ is $1$ .

$x = \pm 1$

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.

$x = 1$

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

$x = - 1$

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

$x = 1, - 1$