Solve for x 80=2(x+5)^2

$80 = 2 {(x + 5)}^{2}$

Step 1

Rewrite the equation as $2 {(x + 5)}^{2} = 80$ .

$2 {(x + 5)}^{2} = 80$

Step 2

Divide each term in $2 {(x + 5)}^{2} = 80$ by $2$ and simplify.

Divide each term in $2 {(x + 5)}^{2} = 80$ by $2$ .

$\frac{2 {(x + 5)}^{2}}{2} = \frac{80}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 5)}^{2}}{2} = \frac{80}{2}$

Divide ${(x + 5)}^{2}$ by $1$ .

${(x + 5)}^{2} = \frac{80}{2}$

Simplify the right side.

Divide $80$ by $2$ .

${(x + 5)}^{2} = 40$

Step 3

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

$x + 5 = \pm \sqrt{40}$

Step 4

Simplify $\pm \sqrt{40}$ .

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x + 5 = \pm \sqrt{4 (10)}$

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

$x + 5 = \pm \sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$x + 5 = \pm 2 \sqrt{10}$

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.

$x + 5 = 2 \sqrt{10}$

Subtract $5$ from both sides of the equation.

$x = 2 \sqrt{10} - 5$

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

$x + 5 = - 2 \sqrt{10}$

Subtract $5$ from both sides of the equation.

$x = - 2 \sqrt{10} - 5$

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

$x = 2 \sqrt{10} - 5, - 2 \sqrt{10} - 5$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{10} - 5, - 2 \sqrt{10} - 5$

Decimal Form:

$x = 1.32455532 \dots, - 11.32455532 \dots$

Solve for x 80=2(x+5)^2

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