y^2+2y+4=36

Solution for y^2+2y+4=36 equation:

Simplifying
y2 + 2y + 4 = 36

Reorder the terms:
4 + 2y + y2 = 36

Solving
4 + 2y + y2 = 36

Solving for variable 'y'.

Reorder the terms:
4 + -36 + 2y + y2 = 36 + -36

Combine like terms: 4 + -36 = -32
-32 + 2y + y2 = 36 + -36

Combine like terms: 36 + -36 = 0
-32 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 2y + 32 + y2 = 0 + 32

Reorder the terms:
-32 + 32 + 2y + y2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 2y + y2 = 0 + 32
2y + y2 = 0 + 32

Combine like terms: 0 + 32 = 32
2y + y2 = 32

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 32 + 1

Reorder the terms:
1 + 2y + y2 = 32 + 1

Combine like terms: 32 + 1 = 33
1 + 2y + y2 = 33

Factor a perfect square on the left side:
(y + 1)(y + 1) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(y + 1) equal to 5.744562647 and -5.744562647.

Subproblem 1
y + 1 = 5.744562647

Simplifying
y + 1 = 5.744562647

Reorder the terms:
1 + y = 5.744562647

Solving
1 + y = 5.744562647

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + y = 5.744562647 + -1
y = 5.744562647 + -1

Combine like terms: 5.744562647 + -1 = 4.744562647
y = 4.744562647

Simplifying
y = 4.744562647

Subproblem 2
y + 1 = -5.744562647

Simplifying
y + 1 = -5.744562647

Reorder the terms:
1 + y = -5.744562647

Solving
1 + y = -5.744562647

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + y = -5.744562647 + -1
y = -5.744562647 + -1

Combine like terms: -5.744562647 + -1 = -6.744562647
y = -6.744562647

Simplifying
y = -6.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.744562647, -6.744562647}