(2y+4)2=36

Take the square root of each side of the equation to set up the solution for y

(2y+4)2⋅12=±36

Remove the perfect root factor 2y+4 under the radical to solve for y.

2y+4=±36

Rewrite 36 as 62.

2y+4=±62

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

2y+4=±6

2y+4=±6

First, use the positive value of the ± to find the first solution.

2y+4=6

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

Subtract 4 from both sides of the equation.

2y=6-4

Subtract 4 from 6.

2y=2

2y=2

Divide each term by 2 and simplify.

Divide each term in 2y=2 by 2.

2y2=22

Cancel the common factor of 2.

Cancel the common factor.

2y2=22

Divide y by 1.

y=22

y=22

Divide 2 by 2.

y=1

y=1

Next, use the negative value of the ± to find the second solution.

2y+4=-6

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

Subtract 4 from both sides of the equation.

2y=-6-4

Subtract 4 from -6.

2y=-10

2y=-10

Divide each term by 2 and simplify.

Divide each term in 2y=-10 by 2.

2y2=-102

Cancel the common factor of 2.

Cancel the common factor.

2y2=-102

Divide y by 1.

y=-102

y=-102

Divide -10 by 2.

y=-5

y=-5

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

y=1,-5

y=1,-5

Solve for y (2y+4)^2=36