Solve Using the Square Root Property 6(x^2-2)=12

$6 (x^{2} - 2) = 12$

Step 1

Divide each term in $6 (x^{2} - 2) = 12$ by $6$ and simplify.

Divide each term in $6 (x^{2} - 2) = 12$ by $6$ .

$\frac{6 (x^{2} - 2)}{6} = \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 (x^{2} - 2)}{6} = \frac{12}{6}$

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

$x^{2} - 2 = \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$x^{2} - 2 = 2$

Step 2

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

Add $2$ to both sides of the equation.

$x^{2} = 2 + 2$

Add $2$ and $2$ .

$x^{2} = 4$

Step 3

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

$x = \pm \sqrt{4}$

Step 4

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$