Solve for y 2(y+4)^2=22

$2 {(y + 4)}^{2} = 22$

Step 1

Divide each term in $2 {(y + 4)}^{2} = 22$ by $2$ and simplify.

Divide each term in $2 {(y + 4)}^{2} = 22$ by $2$ .

$\frac{2 {(y + 4)}^{2}}{2} = \frac{22}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(y + 4)}^{2}}{2} = \frac{22}{2}$

Divide ${(y + 4)}^{2}$ by $1$ .

${(y + 4)}^{2} = \frac{22}{2}$

Simplify the right side.

Divide $22$ by $2$ .

${(y + 4)}^{2} = 11$

Step 2

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

$y + 4 = \pm \sqrt{11}$

Step 3

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.

$y + 4 = \sqrt{11}$

Subtract $4$ from both sides of the equation.

$y = \sqrt{11} - 4$

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

$y + 4 = - \sqrt{11}$

Subtract $4$ from both sides of the equation.

$y = - \sqrt{11} - 4$

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

$y = \sqrt{11} - 4, - \sqrt{11} - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \sqrt{11} - 4, - \sqrt{11} - 4$

Decimal Form:

$y = - 0.68337520 \dots, - 7.31662479 \dots$