y^2+4y=-2

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Solution for y^2+4y=-2 equation: 


Simplifying
y2 + 4y = -2

Reorder the terms:
4y + y2 = -2

Solving
4y + y2 = -2

Solving for variable 'y'.

Reorder the terms:
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 = -0.585786438
y = -0.585786438

Simplifying
y = -0.585786438


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 = -3.414213562
y = -3.414213562

Simplifying
y = -3.414213562


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

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