y^2=2y+2

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Solution for y^2=2y+2 equation:


Simplifying
y2 = 2y + 2

Reorder the terms:
y2 = 2 + 2y

Solving
y2 = 2 + 2y

Solving for variable 'y'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + -2y + y2 = 3

Factor a perfect square on the left side:
(y + -1)(y + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1

y + -1 = 1.732050808 Simplifying y + -1 = 1.732050808 Reorder the terms: -1 + y = 1.732050808 Solving -1 + y = 1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.732050808 + 1 y = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 y = 2.732050808 Simplifying y = 2.732050808

Subproblem 2

y + -1 = -1.732050808 Simplifying y + -1 = -1.732050808 Reorder the terms: -1 + y = -1.732050808 Solving -1 + y = -1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.732050808 + 1 y = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 y = -0.732050808 Simplifying y = -0.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.732050808, -0.732050808}

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