=2y(y-11)-15

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Solution for =2y(y-11)-15 equation: 


Simplifying
0 = 2y(y + -11) + -15

Reorder the terms:
0 = 2y(-11 + y) + -15
0 = (-11 * 2y + y * 2y) + -15
0 = (-22y + 2y2) + -15

Reorder the terms:
0 = -15 + -22y + 2y2

Solving
0 = -15 + -22y + 2y2

Solving for variable 'y'.

Combine like terms: 0 + 15 = 15
15 + 22y + -2y2 = -15 + -22y + 2y2 + 15 + 22y + -2y2

Reorder the terms:
15 + 22y + -2y2 = -15 + 15 + -22y + 22y + 2y2 + -2y2

Combine like terms: -15 + 15 = 0
15 + 22y + -2y2 = 0 + -22y + 22y + 2y2 + -2y2
15 + 22y + -2y2 = -22y + 22y + 2y2 + -2y2

Combine like terms: -22y + 22y = 0
15 + 22y + -2y2 = 0 + 2y2 + -2y2
15 + 22y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
15 + 22y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-7.5 + -11y + y2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -11y + 7.5 + y2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -11y + y2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -11y + y2 = 0 + 7.5
-11y + y2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-11y + y2 = 7.5

The y term is -11y.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11y + 30.25 + y2 = 7.5 + 30.25

Reorder the terms:
30.25 + -11y + y2 = 7.5 + 30.25

Combine like terms: 7.5 + 30.25 = 37.75
30.25 + -11y + y2 = 37.75

Factor a perfect square on the left side:
(y + -5.5)(y + -5.5) = 37.75

Calculate the square root of the right side: 6.144102864

Break this problem into two subproblems by setting 
(y + -5.5) equal to 6.144102864 and -6.144102864.


Subproblem 1
y + -5.5 = 6.144102864

Simplifying
y + -5.5 = 6.144102864

Reorder the terms:
-5.5 + y = 6.144102864

Solving
-5.5 + y = 6.144102864

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = 6.144102864 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = 6.144102864 + 5.5
y = 6.144102864 + 5.5

Combine like terms: 6.144102864 + 5.5 = 11.644102864
y = 11.644102864

Simplifying
y = 11.644102864


Subproblem 2
y + -5.5 = -6.144102864

Simplifying
y + -5.5 = -6.144102864

Reorder the terms:
-5.5 + y = -6.144102864

Solving
-5.5 + y = -6.144102864

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = -6.144102864 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = -6.144102864 + 5.5
y = -6.144102864 + 5.5

Combine like terms: -6.144102864 + 5.5 = -0.644102864
y = -0.644102864

Simplifying
y = -0.644102864


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.644102864, -0.644102864}

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