Solve Using the Square Root Property 2x^2=98

$2 x^{2} = 98$

Step 1

Divide each term in $2 x^{2} = 98$ by $2$ and simplify.

Divide each term in $2 x^{2} = 98$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{98}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{98}{2}$

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

$x^{2} = \frac{98}{2}$

Simplify the right side.

Divide $98$ by $2$ .

$x^{2} = 49$

Step 2

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

$x = \pm \sqrt{49}$

Step 3

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

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

$x = \pm 7$

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.

$x = 7$

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

$x = - 7$

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

$x = 7, - 7$