2y^2+26y=152-60

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Solution for 2y^2+26y=152-60 equation: 


Simplifying
2y2 + 26y = 152 + -60

Reorder the terms:
26y + 2y2 = 152 + -60

Combine like terms: 152 + -60 = 92
26y + 2y2 = 92

Solving
26y + 2y2 = 92

Solving for variable 'y'.

Reorder the terms:
-92 + 26y + 2y2 = 92 + -92

Combine like terms: 92 + -92 = 0
-92 + 26y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + 13y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-46 + 13y + y2)' equal to zero and attempt to solve:

Simplifying
-46 + 13y + y2 = 0

Solving
-46 + 13y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 13y + 46 + y2 = 0 + 46

Reorder the terms:
-46 + 46 + 13y + y2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 13y + y2 = 0 + 46
13y + y2 = 0 + 46

Combine like terms: 0 + 46 = 46
13y + y2 = 46

The y term is 13y.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13y + 42.25 + y2 = 46 + 42.25

Reorder the terms:
42.25 + 13y + y2 = 46 + 42.25

Combine like terms: 46 + 42.25 = 88.25
42.25 + 13y + y2 = 88.25

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 88.25

Calculate the square root of the right side: 9.394147114

Break this problem into two subproblems by setting 
(y + 6.5) equal to 9.394147114 and -9.394147114.


Subproblem 1
y + 6.5 = 9.394147114

Simplifying
y + 6.5 = 9.394147114

Reorder the terms:
6.5 + y = 9.394147114

Solving
6.5 + y = 9.394147114

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = 9.394147114 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 9.394147114 + -6.5
y = 9.394147114 + -6.5

Combine like terms: 9.394147114 + -6.5 = 2.894147114
y = 2.894147114

Simplifying
y = 2.894147114


Subproblem 2
y + 6.5 = -9.394147114

Simplifying
y + 6.5 = -9.394147114

Reorder the terms:
6.5 + y = -9.394147114

Solving
6.5 + y = -9.394147114

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = -9.394147114 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = -9.394147114 + -6.5
y = -9.394147114 + -6.5

Combine like terms: -9.394147114 + -6.5 = -15.894147114
y = -15.894147114

Simplifying
y = -15.894147114


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.894147114, -15.894147114}
Solution
y = {2.894147114, -15.894147114}

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