(y+1)(y-1)+2y=0

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Solution for (y+1)(y-1)+2y=0 equation:


Simplifying
(y + 1)(y + -1) + 2y = 0

Reorder the terms:
(1 + y)(y + -1) + 2y = 0

Reorder the terms:
(1 + y)(-1 + y) + 2y = 0

Multiply (1 + y) * (-1 + y)
(1(-1 + y) + y(-1 + y)) + 2y = 0
((-1 * 1 + y * 1) + y(-1 + y)) + 2y = 0
((-1 + 1y) + y(-1 + y)) + 2y = 0
(-1 + 1y + (-1 * y + y * y)) + 2y = 0
(-1 + 1y + (-1y + y2)) + 2y = 0

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

Reorder the terms:
-1 + 2y + y2 = 0

Solving
-1 + 2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 2y + y2 = 0 + 1

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

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

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 = 1 + 1

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

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

Factor a perfect square on the left side:
(y + 1)(y + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1

y + 1 = 1.414213562 Simplifying y + 1 = 1.414213562 Reorder the terms: 1 + y = 1.414213562 Solving 1 + y = 1.414213562 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 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.414213562 + -1 y = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 y = 0.414213562 Simplifying y = 0.414213562

Subproblem 2

y + 1 = -1.414213562 Simplifying y + 1 = -1.414213562 Reorder the terms: 1 + y = -1.414213562 Solving 1 + y = -1.414213562 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 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.414213562 + -1 y = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 y = -2.414213562 Simplifying y = -2.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.414213562, -2.414213562}

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