y^2-2y-2y-4=96

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Solution for y^2-2y-2y-4=96 equation: 


Simplifying
y2 + -2y + -2y + -4 = 96

Reorder the terms:
-4 + -2y + -2y + y2 = 96

Combine like terms: -2y + -2y = -4y
-4 + -4y + y2 = 96

Solving
-4 + -4y + y2 = 96

Solving for variable 'y'.

Reorder the terms:
-4 + -96 + -4y + y2 = 96 + -96

Combine like terms: -4 + -96 = -100
-100 + -4y + y2 = 96 + -96

Combine like terms: 96 + -96 = 0
-100 + -4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -4y + 100 + y2 = 0 + 100

Reorder the terms:
-100 + 100 + -4y + y2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -4y + y2 = 0 + 100
-4y + y2 = 0 + 100

Combine like terms: 0 + 100 = 100
-4y + y2 = 100

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 100 + 4

Reorder the terms:
4 + -4y + y2 = 100 + 4

Combine like terms: 100 + 4 = 104
4 + -4y + y2 = 104

Factor a perfect square on the left side:
(y + -2)(y + -2) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(y + -2) equal to 10.198039027 and -10.198039027.


Subproblem 1
y + -2 = 10.198039027

Simplifying
y + -2 = 10.198039027

Reorder the terms:
-2 + y = 10.198039027

Solving
-2 + y = 10.198039027

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 10.198039027 + 2

Combine like terms: -2 + 2 = 0
0 + y = 10.198039027 + 2
y = 10.198039027 + 2

Combine like terms: 10.198039027 + 2 = 12.198039027
y = 12.198039027

Simplifying
y = 12.198039027


Subproblem 2
y + -2 = -10.198039027

Simplifying
y + -2 = -10.198039027

Reorder the terms:
-2 + y = -10.198039027

Solving
-2 + y = -10.198039027

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -10.198039027 + 2

Combine like terms: -2 + 2 = 0
0 + y = -10.198039027 + 2
y = -10.198039027 + 2

Combine like terms: -10.198039027 + 2 = -8.198039027
y = -8.198039027

Simplifying
y = -8.198039027


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.198039027, -8.198039027}

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