2(y^2-66+13y)=0

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Solution for 2(y^2-66+13y)=0 equation: 


Simplifying
2(y2 + -66 + 13y) = 0

Reorder the terms:
2(-66 + 13y + y2) = 0
(-66 * 2 + 13y * 2 + y2 * 2) = 0
(-132 + 26y + 2y2) = 0

Solving
-132 + 26y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + 13y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-66 + 13y + y2)' equal to zero and attempt to solve:

Simplifying
-66 + 13y + y2 = 0

Solving
-66 + 13y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 13y + 66 + y2 = 0 + 66

Reorder the terms:
-66 + 66 + 13y + y2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 13y + y2 = 0 + 66
13y + y2 = 0 + 66

Combine like terms: 0 + 66 = 66
13y + y2 = 66

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 = 66 + 42.25

Reorder the terms:
42.25 + 13y + y2 = 66 + 42.25

Combine like terms: 66 + 42.25 = 108.25
42.25 + 13y + y2 = 108.25

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 108.25

Calculate the square root of the right side: 10.404326023

Break this problem into two subproblems by setting 
(y + 6.5) equal to 10.404326023 and -10.404326023.


Subproblem 1
y + 6.5 = 10.404326023

Simplifying
y + 6.5 = 10.404326023

Reorder the terms:
6.5 + y = 10.404326023

Solving
6.5 + y = 10.404326023

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 = 10.404326023 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 10.404326023 + -6.5
y = 10.404326023 + -6.5

Combine like terms: 10.404326023 + -6.5 = 3.904326023
y = 3.904326023

Simplifying
y = 3.904326023


Subproblem 2
y + 6.5 = -10.404326023

Simplifying
y + 6.5 = -10.404326023

Reorder the terms:
6.5 + y = -10.404326023

Solving
6.5 + y = -10.404326023

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 = -10.404326023 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = -10.404326023 + -6.5
y = -10.404326023 + -6.5

Combine like terms: -10.404326023 + -6.5 = -16.904326023
y = -16.904326023

Simplifying
y = -16.904326023


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.904326023, -16.904326023}
Solution
y = {3.904326023, -16.904326023}

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