y^2+8y+8=0

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Solution for y^2+8y+8=0 equation: 


Simplifying
y2 + 8y + 8 = 0

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

Solving
8 + 8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -8 + 16

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

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

Factor a perfect square on the left side:
(y + 4)(y + 4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(y + 4) equal to 2.828427125 and -2.828427125.


Subproblem 1
y + 4 = 2.828427125

Simplifying
y + 4 = 2.828427125

Reorder the terms:
4 + y = 2.828427125

Solving
4 + y = 2.828427125

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 = 2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + y = 2.828427125 + -4
y = 2.828427125 + -4

Combine like terms: 2.828427125 + -4 = -1.171572875
y = -1.171572875

Simplifying
y = -1.171572875


Subproblem 2
y + 4 = -2.828427125

Simplifying
y + 4 = -2.828427125

Reorder the terms:
4 + y = -2.828427125

Solving
4 + y = -2.828427125

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 = -2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + y = -2.828427125 + -4
y = -2.828427125 + -4

Combine like terms: -2.828427125 + -4 = -6.828427125
y = -6.828427125

Simplifying
y = -6.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.171572875, -6.828427125}

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