y^2-12y-8=0

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Solution for y^2-12y-8=0 equation: 


Simplifying
y2 + -12y + -8 = 0

Reorder the terms:
-8 + -12y + y2 = 0

Solving
-8 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -12y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + -12y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -12y + y2 = 0 + 8
-12y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
-12y + y2 = 8

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 = 8 + 36

Reorder the terms:
36 + -12y + y2 = 8 + 36

Combine like terms: 8 + 36 = 44
36 + -12y + y2 = 44

Factor a perfect square on the left side:
(y + -6)(y + -6) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(y + -6) equal to 6.633249581 and -6.633249581.


Subproblem 1
y + -6 = 6.633249581

Simplifying
y + -6 = 6.633249581

Reorder the terms:
-6 + y = 6.633249581

Solving
-6 + y = 6.633249581

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 = 6.633249581 + 6

Combine like terms: -6 + 6 = 0
0 + y = 6.633249581 + 6
y = 6.633249581 + 6

Combine like terms: 6.633249581 + 6 = 12.633249581
y = 12.633249581

Simplifying
y = 12.633249581


Subproblem 2
y + -6 = -6.633249581

Simplifying
y + -6 = -6.633249581

Reorder the terms:
-6 + y = -6.633249581

Solving
-6 + y = -6.633249581

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 = -6.633249581 + 6

Combine like terms: -6 + 6 = 0
0 + y = -6.633249581 + 6
y = -6.633249581 + 6

Combine like terms: -6.633249581 + 6 = -0.633249581
y = -0.633249581

Simplifying
y = -0.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.633249581, -0.633249581}

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