(y^2-12y-36)=1

Solution for (y^2-12y-36)=1 equation:

Simplifying
(y2 + -12y + -36) = 1

Reorder the terms:
(-36 + -12y + y2) = 1

Remove parenthesis around (-36 + -12y + y2)
-36 + -12y + y2 = 1

Solving
-36 + -12y + y2 = 1

Solving for variable 'y'.

Reorder the terms:
-36 + -1 + -12y + y2 = 1 + -1

Combine like terms: -36 + -1 = -37
-37 + -12y + y2 = 1 + -1

Combine like terms: 1 + -1 = 0
-37 + -12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -12y + 37 + y2 = 0 + 37

Reorder the terms:
-37 + 37 + -12y + y2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -12y + y2 = 0 + 37
-12y + y2 = 0 + 37

Combine like terms: 0 + 37 = 37
-12y + y2 = 37

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = 37 + 36

Reorder the terms:
36 + -12y + y2 = 37 + 36

Combine like terms: 37 + 36 = 73
36 + -12y + y2 = 73

Factor a perfect square on the left side:
(y + -6)(y + -6) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(y + -6) equal to 8.544003745 and -8.544003745.

Subproblem 1
y + -6 = 8.544003745

Simplifying
y + -6 = 8.544003745

Reorder the terms:
-6 + y = 8.544003745

Solving
-6 + y = 8.544003745

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = 8.544003745 + 6

Combine like terms: -6 + 6 = 0
0 + y = 8.544003745 + 6
y = 8.544003745 + 6

Combine like terms: 8.544003745 + 6 = 14.544003745
y = 14.544003745

Simplifying
y = 14.544003745

Subproblem 2
y + -6 = -8.544003745

Simplifying
y + -6 = -8.544003745

Reorder the terms:
-6 + y = -8.544003745

Solving
-6 + y = -8.544003745

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = -8.544003745 + 6

Combine like terms: -6 + 6 = 0
0 + y = -8.544003745 + 6
y = -8.544003745 + 6

Combine like terms: -8.544003745 + 6 = -2.544003745
y = -2.544003745

Simplifying
y = -2.544003745

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.544003745, -2.544003745}