Solve Using the Square Root Property 2x^2=242

$2 x^{2} = 242$

Step 1

Divide each term in $2 x^{2} = 242$ by $2$ and simplify.

Divide each term in $2 x^{2} = 242$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{242}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{242}{2}$

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

$x^{2} = \frac{242}{2}$

Simplify the right side.

Divide $242$ by $2$ .

$x^{2} = 121$

Step 2

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

$x = \pm \sqrt{121}$

Step 3

Simplify $\pm \sqrt{121}$ .

Rewrite $121$ as $11^{2}$ .

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

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

$x = \pm 11$

Step 4

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.

$x = 11$

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

$x = - 11$

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

$x = 11, - 11$