Solve Using the Square Root Property 2x^2-9=11

$2 x^{2} - 9 = 11$

Step 1

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

Add $9$ to both sides of the equation.

$2 x^{2} = 11 + 9$

Add $11$ and $9$ .

$2 x^{2} = 20$

Step 2

Divide each term in $2 x^{2} = 20$ by $2$ and simplify.

Divide each term in $2 x^{2} = 20$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{20}{2}$

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

$x^{2} = \frac{20}{2}$

Simplify the right side.

Divide $20$ by $2$ .

$x^{2} = 10$

Step 3

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

$x = \pm \sqrt{10}$

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.

$x = \sqrt{10}$

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

$x = - \sqrt{10}$

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

$x = \sqrt{10}, - \sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{10}, - \sqrt{10}$

Decimal Form:

$x = 3.16227766 \dots, - 3.16227766 \dots$