y^2+13y-36=0

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Solution for y^2+13y-36=0 equation: 


Simplifying
y2 + 13y + -36 = 0

Reorder the terms:
-36 + 13y + y2 = 0

Solving
-36 + 13y + 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 + 13y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + 13y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 13y + y2 = 0 + 36
13y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
13y + y2 = 36

The y term is 13y.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13y + 42.25 + y2 = 36 + 42.25

Reorder the terms:
42.25 + 13y + y2 = 36 + 42.25

Combine like terms: 36 + 42.25 = 78.25
42.25 + 13y + y2 = 78.25

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(y + 6.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
y + 6.5 = 8.845903006

Simplifying
y + 6.5 = 8.845903006

Reorder the terms:
6.5 + y = 8.845903006

Solving
6.5 + y = 8.845903006

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = 8.845903006 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 8.845903006 + -6.5
y = 8.845903006 + -6.5

Combine like terms: 8.845903006 + -6.5 = 2.345903006
y = 2.345903006

Simplifying
y = 2.345903006


Subproblem 2
y + 6.5 = -8.845903006

Simplifying
y + 6.5 = -8.845903006

Reorder the terms:
6.5 + y = -8.845903006

Solving
6.5 + y = -8.845903006

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = -8.845903006 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = -8.845903006 + -6.5
y = -8.845903006 + -6.5

Combine like terms: -8.845903006 + -6.5 = -15.345903006
y = -15.345903006

Simplifying
y = -15.345903006


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.345903006, -15.345903006}

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