2y^2+26y=252-60

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Solution for 2y^2+26y=252-60 equation: 


Simplifying
2y2 + 26y = 252 + -60

Reorder the terms:
26y + 2y2 = 252 + -60

Combine like terms: 252 + -60 = 192
26y + 2y2 = 192

Solving
26y + 2y2 = 192

Solving for variable 'y'.

Reorder the terms:
-192 + 26y + 2y2 = 192 + -192

Combine like terms: 192 + -192 = 0
-192 + 26y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-96 + 13y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-96 + 13y + y2)' equal to zero and attempt to solve:

Simplifying
-96 + 13y + y2 = 0

Solving
-96 + 13y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 13y + 96 + y2 = 0 + 96

Reorder the terms:
-96 + 96 + 13y + y2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 13y + y2 = 0 + 96
13y + y2 = 0 + 96

Combine like terms: 0 + 96 = 96
13y + y2 = 96

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 = 96 + 42.25

Reorder the terms:
42.25 + 13y + y2 = 96 + 42.25

Combine like terms: 96 + 42.25 = 138.25
42.25 + 13y + y2 = 138.25

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 138.25

Calculate the square root of the right side: 11.757976016

Break this problem into two subproblems by setting 
(y + 6.5) equal to 11.757976016 and -11.757976016.


Subproblem 1
y + 6.5 = 11.757976016

Simplifying
y + 6.5 = 11.757976016

Reorder the terms:
6.5 + y = 11.757976016

Solving
6.5 + y = 11.757976016

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 = 11.757976016 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 11.757976016 + -6.5
y = 11.757976016 + -6.5

Combine like terms: 11.757976016 + -6.5 = 5.257976016
y = 5.257976016

Simplifying
y = 5.257976016


Subproblem 2
y + 6.5 = -11.757976016

Simplifying
y + 6.5 = -11.757976016

Reorder the terms:
6.5 + y = -11.757976016

Solving
6.5 + y = -11.757976016

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 = -11.757976016 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = -11.757976016 + -6.5
y = -11.757976016 + -6.5

Combine like terms: -11.757976016 + -6.5 = -18.257976016
y = -18.257976016

Simplifying
y = -18.257976016


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.257976016, -18.257976016}
Solution
y = {5.257976016, -18.257976016}

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