w^2+8w-1=0

Solution for w^2+8w-1=0 equation:

Simplifying
w2 + 8w + -1 = 0

Reorder the terms:
-1 + 8w + w2 = 0

Solving
-1 + 8w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 8w + 1 + w2 = 0 + 1

Reorder the terms:
-1 + 1 + 8w + w2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8w + w2 = 0 + 1
8w + w2 = 0 + 1

Combine like terms: 0 + 1 = 1
8w + w2 = 1

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

Add '16' to each side of the equation.
8w + 16 + w2 = 1 + 16

Reorder the terms:
16 + 8w + w2 = 1 + 16

Combine like terms: 1 + 16 = 17
16 + 8w + w2 = 17

Factor a perfect square on the left side:
(w + 4)(w + 4) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(w + 4) equal to 4.123105626 and -4.123105626.

Subproblem 1
w + 4 = 4.123105626

Simplifying
w + 4 = 4.123105626

Reorder the terms:
4 + w = 4.123105626

Solving
4 + w = 4.123105626

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = 4.123105626 + -4

Combine like terms: 4 + -4 = 0
0 + w = 4.123105626 + -4
w = 4.123105626 + -4

Combine like terms: 4.123105626 + -4 = 0.123105626
w = 0.123105626

Simplifying
w = 0.123105626

Subproblem 2
w + 4 = -4.123105626

Simplifying
w + 4 = -4.123105626

Reorder the terms:
4 + w = -4.123105626

Solving
4 + w = -4.123105626

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = -4.123105626 + -4

Combine like terms: 4 + -4 = 0
0 + w = -4.123105626 + -4
w = -4.123105626 + -4

Combine like terms: -4.123105626 + -4 = -8.123105626
w = -8.123105626

Simplifying
w = -8.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.123105626, -8.123105626}