2y(y-1)=5

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Solution for 2y(y-1)=5 equation: 


Simplifying
2y(y + -1) = 5

Reorder the terms:
2y(-1 + y) = 5
(-1 * 2y + y * 2y) = 5
(-2y + 2y2) = 5

Solving
-2y + 2y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + -2y + 2y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -2y + 2y2 = 0

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

Divide each side by '2'.
-2.5 + -1y + y2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -1y + 2.5 + y2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -1y + y2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -1y + y2 = 0 + 2.5
-1y + y2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-1y + y2 = 2.5

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 = 2.5 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + -1y + y2 = 2.75

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(y + -0.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
y + -0.5 = 1.658312395

Simplifying
y + -0.5 = 1.658312395

Reorder the terms:
-0.5 + y = 1.658312395

Solving
-0.5 + y = 1.658312395

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 = 1.658312395 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 1.658312395 + 0.5
y = 1.658312395 + 0.5

Combine like terms: 1.658312395 + 0.5 = 2.158312395
y = 2.158312395

Simplifying
y = 2.158312395


Subproblem 2
y + -0.5 = -1.658312395

Simplifying
y + -0.5 = -1.658312395

Reorder the terms:
-0.5 + y = -1.658312395

Solving
-0.5 + y = -1.658312395

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 = -1.658312395 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -1.658312395 + 0.5
y = -1.658312395 + 0.5

Combine like terms: -1.658312395 + 0.5 = -1.158312395
y = -1.158312395

Simplifying
y = -1.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.158312395, -1.158312395}

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