Solve Using the Square Root Property 24=3(x^2+7)

$24 = 3 (x^{2} + 7)$

Step 1

Rewrite the equation as $3 (x^{2} + 7) = 24$ .

$3 (x^{2} + 7) = 24$

Step 2

Divide each term in $3 (x^{2} + 7) = 24$ by $3$ and simplify.

Divide each term in $3 (x^{2} + 7) = 24$ by $3$ .

$\frac{3 (x^{2} + 7)}{3} = \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x^{2} + 7)}{3} = \frac{24}{3}$

Divide $x^{2} + 7$ by $1$ .

$x^{2} + 7 = \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

$x^{2} + 7 = 8$

Step 3

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

Subtract $7$ from both sides of the equation.

$x^{2} = 8 - 7$

Subtract $7$ from $8$ .

$x^{2} = 1$

Step 4

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

$x = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$x = \pm 1$

Step 6

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.

$x = 1, - 1$