y^2+8y=-2

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Solution for y^2+8y=-2 equation: 


Simplifying
y2 + 8y = -2

Reorder the terms:
8y + y2 = -2

Solving
8y + y2 = -2

Solving for variable 'y'.

Reorder the terms:
2 + 8y + y2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 8y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 8y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 8y + y2 = 0 + -2
8y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
8y + y2 = -2

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = -2 + 16

Reorder the terms:
16 + 8y + y2 = -2 + 16

Combine like terms: -2 + 16 = 14
16 + 8y + y2 = 14

Factor a perfect square on the left side:
(y + 4)(y + 4) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(y + 4) equal to 3.741657387 and -3.741657387.


Subproblem 1
y + 4 = 3.741657387

Simplifying
y + 4 = 3.741657387

Reorder the terms:
4 + y = 3.741657387

Solving
4 + y = 3.741657387

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 3.741657387 + -4

Combine like terms: 4 + -4 = 0
0 + y = 3.741657387 + -4
y = 3.741657387 + -4

Combine like terms: 3.741657387 + -4 = -0.258342613
y = -0.258342613

Simplifying
y = -0.258342613


Subproblem 2
y + 4 = -3.741657387

Simplifying
y + 4 = -3.741657387

Reorder the terms:
4 + y = -3.741657387

Solving
4 + y = -3.741657387

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -3.741657387 + -4

Combine like terms: 4 + -4 = 0
0 + y = -3.741657387 + -4
y = -3.741657387 + -4

Combine like terms: -3.741657387 + -4 = -7.741657387
y = -7.741657387

Simplifying
y = -7.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.258342613, -7.741657387}

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