w^2-6w+2=0

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

Simplifying
w2 + -6w + 2 = 0

Reorder the terms:
2 + -6w + w2 = 0

Solving
2 + -6w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6w + -2 + w2 = 0 + -2

Reorder the terms:
2 + -2 + -6w + w2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6w + w2 = 0 + -2
-6w + w2 = 0 + -2

Combine like terms: 0 + -2 = -2
-6w + w2 = -2

The w term is -6w.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6w + 9 + w2 = -2 + 9

Reorder the terms:
9 + -6w + w2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6w + w2 = 7

Factor a perfect square on the left side:
(w + -3)(w + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(w + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1
w + -3 = 2.645751311

Simplifying
w + -3 = 2.645751311

Reorder the terms:
-3 + w = 2.645751311

Solving
-3 + w = 2.645751311

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = 2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + w = 2.645751311 + 3
w = 2.645751311 + 3

Combine like terms: 2.645751311 + 3 = 5.645751311
w = 5.645751311

Simplifying
w = 5.645751311

Subproblem 2
w + -3 = -2.645751311

Simplifying
w + -3 = -2.645751311

Reorder the terms:
-3 + w = -2.645751311

Solving
-3 + w = -2.645751311

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = -2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + w = -2.645751311 + 3
w = -2.645751311 + 3

Combine like terms: -2.645751311 + 3 = 0.354248689
w = 0.354248689

Simplifying
w = 0.354248689

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.645751311, 0.354248689}