(y-2)(y-2)=2

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


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

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

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

Multiply (-2 + y) * (-2 + y)
(-2(-2 + y) + y(-2 + y)) = 2
((-2 * -2 + y * -2) + y(-2 + y)) = 2
((4 + -2y) + y(-2 + y)) = 2
(4 + -2y + (-2 * y + y * y)) = 2
(4 + -2y + (-2y + y2)) = 2

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

Solving
4 + -4y + y2 = 2

Solving for variable 'y'.

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

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

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

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