w^2-8w+6=0

Solution for w^2-8w+6=0 equation:

Simplifying
w2 + -8w + 6 = 0

Reorder the terms:
6 + -8w + w2 = 0

Solving
6 + -8w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8w + -6 + w2 = 0 + -6

Reorder the terms:
6 + -6 + -8w + w2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8w + w2 = 0 + -6
-8w + w2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8w + w2 = -6

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 = -6 + 16

Reorder the terms:
16 + -8w + w2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8w + w2 = 10

Factor a perfect square on the left side:
(w + -4)(w + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(w + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1
w + -4 = 3.16227766

Simplifying
w + -4 = 3.16227766

Reorder the terms:
-4 + w = 3.16227766

Solving
-4 + w = 3.16227766

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 = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + w = 3.16227766 + 4
w = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
w = 7.16227766

Simplifying
w = 7.16227766

Subproblem 2
w + -4 = -3.16227766

Simplifying
w + -4 = -3.16227766

Reorder the terms:
-4 + w = -3.16227766

Solving
-4 + w = -3.16227766

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 = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + w = -3.16227766 + 4
w = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
w = 0.83772234

Simplifying
w = 0.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.16227766, 0.83772234}