y^2+8y+1=0

Solution for y^2+8y+1=0 equation:

Simplifying
y2 + 8y + 1 = 0

Reorder the terms:
1 + 8y + y2 = 0

Solving
1 + 8y + 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 + 8y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + 8y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8y + y2 = 0 + -1
8y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
8y + y2 = -1

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 = -1 + 16

Reorder the terms:
16 + 8y + y2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + 8y + y2 = 15

Factor a perfect square on the left side:
(y + 4)(y + 4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(y + 4) equal to 3.872983346 and -3.872983346.

Subproblem 1
y + 4 = 3.872983346

Simplifying
y + 4 = 3.872983346

Reorder the terms:
4 + y = 3.872983346

Solving
4 + y = 3.872983346

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 = 3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + y = 3.872983346 + -4
y = 3.872983346 + -4

Combine like terms: 3.872983346 + -4 = -0.127016654
y = -0.127016654

Simplifying
y = -0.127016654

Subproblem 2
y + 4 = -3.872983346

Simplifying
y + 4 = -3.872983346

Reorder the terms:
4 + y = -3.872983346

Solving
4 + y = -3.872983346

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 = -3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + y = -3.872983346 + -4
y = -3.872983346 + -4

Combine like terms: -3.872983346 + -4 = -7.872983346
y = -7.872983346

Simplifying
y = -7.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.127016654, -7.872983346}