2y^2-2y-44=0

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Solution for 2y^2-2y-44=0 equation: 


Simplifying
2y2 + -2y + -44 = 0

Reorder the terms:
-44 + -2y + 2y2 = 0

Solving
-44 + -2y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + -1y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-22 + -1y + y2)' equal to zero and attempt to solve:

Simplifying
-22 + -1y + y2 = 0

Solving
-22 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -1y + 22 + y2 = 0 + 22

Reorder the terms:
-22 + 22 + -1y + y2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1y + y2 = 0 + 22
-1y + y2 = 0 + 22

Combine like terms: 0 + 22 = 22
-1y + y2 = 22

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 22 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 22 + 0.25

Combine like terms: 22 + 0.25 = 22.25
0.25 + -1y + y2 = 22.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(y + -0.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
y + -0.5 = 4.716990566

Simplifying
y + -0.5 = 4.716990566

Reorder the terms:
-0.5 + y = 4.716990566

Solving
-0.5 + y = 4.716990566

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 4.716990566 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 4.716990566 + 0.5
y = 4.716990566 + 0.5

Combine like terms: 4.716990566 + 0.5 = 5.216990566
y = 5.216990566

Simplifying
y = 5.216990566


Subproblem 2
y + -0.5 = -4.716990566

Simplifying
y + -0.5 = -4.716990566

Reorder the terms:
-0.5 + y = -4.716990566

Solving
-0.5 + y = -4.716990566

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -4.716990566 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -4.716990566 + 0.5
y = -4.716990566 + 0.5

Combine like terms: -4.716990566 + 0.5 = -4.216990566
y = -4.216990566

Simplifying
y = -4.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.216990566, -4.216990566}
Solution
y = {5.216990566, -4.216990566}

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