Solve Using the Square Root Property 2x^2+11=131

$2 x^{2} + 11 = 131$

Step 1

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

Subtract $11$ from both sides of the equation.

$2 x^{2} = 131 - 11$

Subtract $11$ from $131$ .

$2 x^{2} = 120$

Step 2

Divide each term in $2 x^{2} = 120$ by $2$ and simplify.

Divide each term in $2 x^{2} = 120$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{120}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{120}{2}$

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

$x^{2} = \frac{120}{2}$

Simplify the right side.

Divide $120$ by $2$ .

$x^{2} = 60$

Step 3

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

$x = \pm \sqrt{60}$

Step 4

Simplify $\pm \sqrt{60}$ .

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$x = \pm \sqrt{4 (15)}$

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

$x = \pm \sqrt{2^{2} \cdot 15}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{15}$

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.

$x = 2 \sqrt{15}$

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

$x = - 2 \sqrt{15}$

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

$x = 2 \sqrt{15}, - 2 \sqrt{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{15}, - 2 \sqrt{15}$

Decimal Form:

$x = 7.74596669 \dots, - 7.74596669 \dots$

Solve Using the Square Root Property 2x^2+11=131

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