y^2-12y-5=0

Solution for y^2-12y-5=0 equation:

Simplifying
y2 + -12y + -5 = 0

Reorder the terms:
-5 + -12y + y2 = 0

Solving
-5 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -12y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + -12y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -12y + y2 = 0 + 5
-12y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
-12y + y2 = 5

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 = 5 + 36

Reorder the terms:
36 + -12y + y2 = 5 + 36

Combine like terms: 5 + 36 = 41
36 + -12y + y2 = 41

Factor a perfect square on the left side:
(y + -6)(y + -6) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(y + -6) equal to 6.403124237 and -6.403124237.

Subproblem 1
y + -6 = 6.403124237

Simplifying
y + -6 = 6.403124237

Reorder the terms:
-6 + y = 6.403124237

Solving
-6 + y = 6.403124237

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 = 6.403124237 + 6

Combine like terms: -6 + 6 = 0
0 + y = 6.403124237 + 6
y = 6.403124237 + 6

Combine like terms: 6.403124237 + 6 = 12.403124237
y = 12.403124237

Simplifying
y = 12.403124237

Subproblem 2
y + -6 = -6.403124237

Simplifying
y + -6 = -6.403124237

Reorder the terms:
-6 + y = -6.403124237

Solving
-6 + y = -6.403124237

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 = -6.403124237 + 6

Combine like terms: -6 + 6 = 0
0 + y = -6.403124237 + 6
y = -6.403124237 + 6

Combine like terms: -6.403124237 + 6 = -0.403124237
y = -0.403124237

Simplifying
y = -0.403124237

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.403124237, -0.403124237}