y^2+y=96

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Solution for y^2+y=96 equation: 


Simplifying
y2 + y = 96

Reorder the terms:
y + y2 = 96

Solving
y + y2 = 96

Solving for variable 'y'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
y + 0.25 + y2 = 96 + 0.25

Reorder the terms:
0.25 + y + y2 = 96 + 0.25

Combine like terms: 96 + 0.25 = 96.25
0.25 + y + y2 = 96.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(y + 0.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
y + 0.5 = 9.810708435

Simplifying
y + 0.5 = 9.810708435

Reorder the terms:
0.5 + y = 9.810708435

Solving
0.5 + y = 9.810708435

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 9.810708435 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 9.810708435 + -0.5
y = 9.810708435 + -0.5

Combine like terms: 9.810708435 + -0.5 = 9.310708435
y = 9.310708435

Simplifying
y = 9.310708435


Subproblem 2
y + 0.5 = -9.810708435

Simplifying
y + 0.5 = -9.810708435

Reorder the terms:
0.5 + y = -9.810708435

Solving
0.5 + y = -9.810708435

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -9.810708435 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -9.810708435 + -0.5
y = -9.810708435 + -0.5

Combine like terms: -9.810708435 + -0.5 = -10.310708435
y = -10.310708435

Simplifying
y = -10.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.310708435, -10.310708435}

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