Solve Using the Square Root Property 2x^2-88=0

$2 x^{2} - 88 = 0$

Step 1

Add $88$ to both sides of the equation.

$2 x^{2} = 88$

Step 2

Divide each term in $2 x^{2} = 88$ by $2$ and simplify.

Divide each term in $2 x^{2} = 88$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{88}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{88}{2}$

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

$x^{2} = \frac{88}{2}$

Simplify the right side.

Divide $88$ by $2$ .

$x^{2} = 44$

Step 3

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

$x = \pm \sqrt{44}$

Step 4

Simplify $\pm \sqrt{44}$ .

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$x = \pm \sqrt{4 (11)}$

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

$x = \pm \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{11}$

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.

$x = 2 \sqrt{11}$

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

$x = - 2 \sqrt{11}$

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

$x = 2 \sqrt{11}, - 2 \sqrt{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{11}, - 2 \sqrt{11}$

Decimal Form:

$x = 6.63324958 \dots, - 6.63324958 \dots$