y^2+8y-36=0

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Solution for y^2+8y-36=0 equation: 


Simplifying
y2 + 8y + -36 = 0

Reorder the terms:
-36 + 8y + y2 = 0

Solving
-36 + 8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 8y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + 8y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 8y + y2 = 0 + 36
8y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
8y + y2 = 36

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 = 36 + 16

Reorder the terms:
16 + 8y + y2 = 36 + 16

Combine like terms: 36 + 16 = 52
16 + 8y + y2 = 52

Factor a perfect square on the left side:
(y + 4)(y + 4) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(y + 4) equal to 7.211102551 and -7.211102551.


Subproblem 1
y + 4 = 7.211102551

Simplifying
y + 4 = 7.211102551

Reorder the terms:
4 + y = 7.211102551

Solving
4 + y = 7.211102551

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 = 7.211102551 + -4

Combine like terms: 4 + -4 = 0
0 + y = 7.211102551 + -4
y = 7.211102551 + -4

Combine like terms: 7.211102551 + -4 = 3.211102551
y = 3.211102551

Simplifying
y = 3.211102551


Subproblem 2
y + 4 = -7.211102551

Simplifying
y + 4 = -7.211102551

Reorder the terms:
4 + y = -7.211102551

Solving
4 + y = -7.211102551

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 = -7.211102551 + -4

Combine like terms: 4 + -4 = 0
0 + y = -7.211102551 + -4
y = -7.211102551 + -4

Combine like terms: -7.211102551 + -4 = -11.211102551
y = -11.211102551

Simplifying
y = -11.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.211102551, -11.211102551}

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