Solve Using the Square Root Property 1/2x^2-8=0

$\frac{1}{2} x^{2} - 8 = 0$

Step 1

Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{2}}{2} - 8 = 0$

Step 2

Add $8$ to both sides of the equation.

$\frac{x^{2}}{2} = 8$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{x^{2}}{2} = 2 \cdot 8$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x^{2}}{2} = 2 \cdot 8$

Rewrite the expression.

$x^{2} = 2 \cdot 8$

Simplify the right side.

Multiply $2$ by $8$ .

$x^{2} = 16$

Step 5

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

$x = \pm \sqrt{16}$

Step 6

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

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

$x = \pm 4$

Step 7

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.

$x = 4$

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

$x = - 4$

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

$x = 4, - 4$