2y*2y-18y+44=(y-7)(y-7)

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Solution for 2y*2y-18y+44=(y-7)(y-7) equation: 


Simplifying
2y * 2y + -18y + 44 = (y + -7)(y + -7)

Reorder the terms for easier multiplication:
2 * 2y * y + -18y + 44 = (y + -7)(y + -7)

Multiply 2 * 2
4y * y + -18y + 44 = (y + -7)(y + -7)

Multiply y * y
4y2 + -18y + 44 = (y + -7)(y + -7)

Reorder the terms:
44 + -18y + 4y2 = (y + -7)(y + -7)

Reorder the terms:
44 + -18y + 4y2 = (-7 + y)(y + -7)

Reorder the terms:
44 + -18y + 4y2 = (-7 + y)(-7 + y)

Multiply (-7 + y) * (-7 + y)
44 + -18y + 4y2 = (-7(-7 + y) + y(-7 + y))
44 + -18y + 4y2 = ((-7 * -7 + y * -7) + y(-7 + y))
44 + -18y + 4y2 = ((49 + -7y) + y(-7 + y))
44 + -18y + 4y2 = (49 + -7y + (-7 * y + y * y))
44 + -18y + 4y2 = (49 + -7y + (-7y + y2))

Combine like terms: -7y + -7y = -14y
44 + -18y + 4y2 = (49 + -14y + y2)

Solving
44 + -18y + 4y2 = 49 + -14y + y2

Solving for variable 'y'.

Reorder the terms:
44 + -49 + -18y + 14y + 4y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: 44 + -49 = -5
-5 + -18y + 14y + 4y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: -18y + 14y = -4y
-5 + -4y + 4y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: 4y2 + -1y2 = 3y2
-5 + -4y + 3y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Reorder the terms:
-5 + -4y + 3y2 = 49 + -49 + -14y + 14y + y2 + -1y2

Combine like terms: 49 + -49 = 0
-5 + -4y + 3y2 = 0 + -14y + 14y + y2 + -1y2
-5 + -4y + 3y2 = -14y + 14y + y2 + -1y2

Combine like terms: -14y + 14y = 0
-5 + -4y + 3y2 = 0 + y2 + -1y2
-5 + -4y + 3y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-5 + -4y + 3y2 = 0

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

Divide each side by '3'.
-1.666666667 + -1.333333333y + y2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1.333333333y + 1.666666667 + y2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1.333333333y + y2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1.333333333y + y2 = 0 + 1.666666667
-1.333333333y + y2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1.333333333y + y2 = 1.666666667

The y term is -1.333333333y.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333y + 0.4444444442 + y2 = 1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333y + y2 = 1.666666667 + 0.4444444442

Combine like terms: 1.666666667 + 0.4444444442 = 2.1111111112
0.4444444442 + -1.333333333y + y2 = 2.1111111112

Factor a perfect square on the left side:
(y + -0.6666666665)(y + -0.6666666665) = 2.1111111112

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(y + -0.6666666665) equal to 1.452966315 and -1.452966315.


Subproblem 1
y + -0.6666666665 = 1.452966315

Simplifying
y + -0.6666666665 = 1.452966315

Reorder the terms:
-0.6666666665 + y = 1.452966315

Solving
-0.6666666665 + y = 1.452966315

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = 1.452966315 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = 1.452966315 + 0.6666666665
y = 1.452966315 + 0.6666666665

Combine like terms: 1.452966315 + 0.6666666665 = 2.1196329815
y = 2.1196329815

Simplifying
y = 2.1196329815


Subproblem 2
y + -0.6666666665 = -1.452966315

Simplifying
y + -0.6666666665 = -1.452966315

Reorder the terms:
-0.6666666665 + y = -1.452966315

Solving
-0.6666666665 + y = -1.452966315

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = -1.452966315 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = -1.452966315 + 0.6666666665
y = -1.452966315 + 0.6666666665

Combine like terms: -1.452966315 + 0.6666666665 = -0.7862996485
y = -0.7862996485

Simplifying
y = -0.7862996485


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.1196329815, -0.7862996485}

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