2(y+4)(y+4)=22

Solution for 2(y+4)(y+4)=22 equation:

Simplifying
2(y + 4)(y + 4) = 22

Reorder the terms:
2(4 + y)(y + 4) = 22

Reorder the terms:
2(4 + y)(4 + y) = 22

Multiply (4 + y) * (4 + y)
2(4(4 + y) + y(4 + y)) = 22
2((4 * 4 + y * 4) + y(4 + y)) = 22
2((16 + 4y) + y(4 + y)) = 22
2(16 + 4y + (4 * y + y * y)) = 22
2(16 + 4y + (4y + y2)) = 22

Combine like terms: 4y + 4y = 8y
2(16 + 8y + y2) = 22
(16 * 2 + 8y * 2 + y2 * 2) = 22
(32 + 16y + 2y2) = 22

Solving
32 + 16y + 2y2 = 22

Solving for variable 'y'.

Reorder the terms:
32 + -22 + 16y + 2y2 = 22 + -22

Combine like terms: 32 + -22 = 10
10 + 16y + 2y2 = 22 + -22

Combine like terms: 22 + -22 = 0
10 + 16y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 8y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 8y + y2)' equal to zero and attempt to solve:

Simplifying
5 + 8y + y2 = 0

Solving
5 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + 8y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8y + y2 = 0 + -5
8y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
8y + y2 = -5

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = -5 + 16

Reorder the terms:
16 + 8y + y2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + 8y + y2 = 11

Factor a perfect square on the left side:
(y + 4)(y + 4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(y + 4) equal to 3.31662479 and -3.31662479.

Subproblem 1
y + 4 = 3.31662479

Simplifying
y + 4 = 3.31662479

Reorder the terms:
4 + y = 3.31662479

Solving
4 + y = 3.31662479

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + y = 3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + y = 3.31662479 + -4
y = 3.31662479 + -4

Combine like terms: 3.31662479 + -4 = -0.68337521
y = -0.68337521

Simplifying
y = -0.68337521

Subproblem 2
y + 4 = -3.31662479

Simplifying
y + 4 = -3.31662479

Reorder the terms:
4 + y = -3.31662479

Solving
4 + y = -3.31662479

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + y = -3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + y = -3.31662479 + -4
y = -3.31662479 + -4

Combine like terms: -3.31662479 + -4 = -7.31662479
y = -7.31662479

Simplifying
y = -7.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.68337521, -7.31662479}
Solution
y = {-0.68337521, -7.31662479}