Solve Using the Square Root Property 2(x^2-7)-2=2

$2 (x^{2} - 7) - 2 = 2$

Step 1

Simplify $2 (x^{2} - 7) - 2$ .

Simplify each term.

Apply the distributive property.

$2 x^{2} + 2 \cdot - 7 - 2 = 2$

Multiply $2$ by $- 7$ .

$2 x^{2} - 14 - 2 = 2$

Subtract $2$ from $- 14$ .

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

Step 2

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

Add $16$ to both sides of the equation.

$2 x^{2} = 2 + 16$

Add $2$ and $16$ .

$2 x^{2} = 18$

Step 3

Divide each term in $2 x^{2} = 18$ by $2$ and simplify.

Divide each term in $2 x^{2} = 18$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{18}{2}$

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

$x^{2} = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$x^{2} = 9$

Step 4

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

$x = \pm \sqrt{9}$

Step 5

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

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

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

Solve Using the Square Root Property 2(x^2-7)-2=2

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