2(y-1)(y-1)=y^2

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

Simplifying
2(y + -1)(y + -1) = y2

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

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

Multiply (-1 + y) * (-1 + y)
2(-1(-1 + y) + y(-1 + y)) = y2
2((-1 * -1 + y * -1) + y(-1 + y)) = y2
2((1 + -1y) + y(-1 + y)) = y2
2(1 + -1y + (-1 * y + y * y)) = y2
2(1 + -1y + (-1y + y2)) = y2

Combine like terms: -1y + -1y = -2y
2(1 + -2y + y2) = y2
(1 * 2 + -2y * 2 + y2 * 2) = y2
(2 + -4y + 2y2) = y2

Solving
2 + -4y + 2y2 = y2

Solving for variable 'y'.

Combine like terms: 2y2 + -1y2 = 1y2
2 + -4y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
2 + -4y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -4y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4y + y2 = 0 + -2
-4y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4y + y2 = -2

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -2 + 4

Reorder the terms:
4 + -4y + y2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4y + y2 = 2

Factor a perfect square on the left side:
(y + -2)(y + -2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + -2) equal to 1.414213562 and -1.414213562.

Subproblem 1
y + -2 = 1.414213562

Simplifying
y + -2 = 1.414213562

Reorder the terms:
-2 + y = 1.414213562

Solving
-2 + y = 1.414213562

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + y = 1.414213562 + 2
y = 1.414213562 + 2

Combine like terms: 1.414213562 + 2 = 3.414213562
y = 3.414213562

Simplifying
y = 3.414213562

Subproblem 2
y + -2 = -1.414213562

Simplifying
y + -2 = -1.414213562

Reorder the terms:
-2 + y = -1.414213562

Solving
-2 + y = -1.414213562

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + y = -1.414213562 + 2
y = -1.414213562 + 2

Combine like terms: -1.414213562 + 2 = 0.585786438
y = 0.585786438

Simplifying
y = 0.585786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.414213562, 0.585786438}