4y^2+64y-116=0

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Solution for 4y^2+64y-116=0 equation: 


Simplifying
4y2 + 64y + -116 = 0

Reorder the terms:
-116 + 64y + 4y2 = 0

Solving
-116 + 64y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-29 + 16y + y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-29 + 16y + y2)' equal to zero and attempt to solve:

Simplifying
-29 + 16y + y2 = 0

Solving
-29 + 16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 16y + 29 + y2 = 0 + 29

Reorder the terms:
-29 + 29 + 16y + y2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 16y + y2 = 0 + 29
16y + y2 = 0 + 29

Combine like terms: 0 + 29 = 29
16y + y2 = 29

The y term is 16y.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16y + 64 + y2 = 29 + 64

Reorder the terms:
64 + 16y + y2 = 29 + 64

Combine like terms: 29 + 64 = 93
64 + 16y + y2 = 93

Factor a perfect square on the left side:
(y + 8)(y + 8) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(y + 8) equal to 9.643650761 and -9.643650761.


Subproblem 1
y + 8 = 9.643650761

Simplifying
y + 8 = 9.643650761

Reorder the terms:
8 + y = 9.643650761

Solving
8 + y = 9.643650761

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = 9.643650761 + -8

Combine like terms: 8 + -8 = 0
0 + y = 9.643650761 + -8
y = 9.643650761 + -8

Combine like terms: 9.643650761 + -8 = 1.643650761
y = 1.643650761

Simplifying
y = 1.643650761


Subproblem 2
y + 8 = -9.643650761

Simplifying
y + 8 = -9.643650761

Reorder the terms:
8 + y = -9.643650761

Solving
8 + y = -9.643650761

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = -9.643650761 + -8

Combine like terms: 8 + -8 = 0
0 + y = -9.643650761 + -8
y = -9.643650761 + -8

Combine like terms: -9.643650761 + -8 = -17.643650761
y = -17.643650761

Simplifying
y = -17.643650761


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.643650761, -17.643650761}
Solution
y = {1.643650761, -17.643650761}

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