y^2+8y-96=0

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Solution for y^2+8y-96=0 equation: 


Simplifying
y2 + 8y + -96 = 0

Reorder the terms:
-96 + 8y + y2 = 0

Solving
-96 + 8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 8y + 96 + y2 = 0 + 96

Reorder the terms:
-96 + 96 + 8y + y2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 8y + y2 = 0 + 96
8y + y2 = 0 + 96

Combine like terms: 0 + 96 = 96
8y + y2 = 96

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 96 + 16

Reorder the terms:
16 + 8y + y2 = 96 + 16

Combine like terms: 96 + 16 = 112
16 + 8y + y2 = 112

Factor a perfect square on the left side:
(y + 4)(y + 4) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(y + 4) equal to 10.583005244 and -10.583005244.


Subproblem 1
y + 4 = 10.583005244

Simplifying
y + 4 = 10.583005244

Reorder the terms:
4 + y = 10.583005244

Solving
4 + y = 10.583005244

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 10.583005244 + -4

Combine like terms: 4 + -4 = 0
0 + y = 10.583005244 + -4
y = 10.583005244 + -4

Combine like terms: 10.583005244 + -4 = 6.583005244
y = 6.583005244

Simplifying
y = 6.583005244


Subproblem 2
y + 4 = -10.583005244

Simplifying
y + 4 = -10.583005244

Reorder the terms:
4 + y = -10.583005244

Solving
4 + y = -10.583005244

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -10.583005244 + -4

Combine like terms: 4 + -4 = 0
0 + y = -10.583005244 + -4
y = -10.583005244 + -4

Combine like terms: -10.583005244 + -4 = -14.583005244
y = -14.583005244

Simplifying
y = -14.583005244


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.583005244, -14.583005244}

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