y^2-y=36

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Solution for y^2-y=36 equation: 


Simplifying
y2 + -1y = 36

Reorder the terms:
-1y + y2 = 36

Solving
-1y + y2 = 36

Solving for variable 'y'.

Reorder the terms:
-36 + -1y + y2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -1y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + -1y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1y + y2 = 0 + 36
-1y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
-1y + y2 = 36

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 36 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
0.25 + -1y + y2 = 36.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(y + -0.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
y + -0.5 = 6.020797289

Simplifying
y + -0.5 = 6.020797289

Reorder the terms:
-0.5 + y = 6.020797289

Solving
-0.5 + y = 6.020797289

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 6.020797289 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 6.020797289 + 0.5
y = 6.020797289 + 0.5

Combine like terms: 6.020797289 + 0.5 = 6.520797289
y = 6.520797289

Simplifying
y = 6.520797289


Subproblem 2
y + -0.5 = -6.020797289

Simplifying
y + -0.5 = -6.020797289

Reorder the terms:
-0.5 + y = -6.020797289

Solving
-0.5 + y = -6.020797289

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -6.020797289 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -6.020797289 + 0.5
y = -6.020797289 + 0.5

Combine like terms: -6.020797289 + 0.5 = -5.520797289
y = -5.520797289

Simplifying
y = -5.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.520797289, -5.520797289}

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