7w^2-14w+2=0

Solution for 7w^2-14w+2=0 equation:

Simplifying
7w2 + -14w + 2 = 0

Reorder the terms:
2 + -14w + 7w2 = 0

Solving
2 + -14w + 7w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
0.2857142857 + -2w + w2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -2w + -0.2857142857 + w2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -2w + w2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -2w + w2 = 0 + -0.2857142857
-2w + w2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-2w + w2 = -0.2857142857

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = -0.2857142857 + 1

Reorder the terms:
1 + -2w + w2 = -0.2857142857 + 1

Combine like terms: -0.2857142857 + 1 = 0.7142857143
1 + -2w + w2 = 0.7142857143

Factor a perfect square on the left side:
(w + -1)(w + -1) = 0.7142857143

Calculate the square root of the right side: 0.845154255

Break this problem into two subproblems by setting 
(w + -1) equal to 0.845154255 and -0.845154255.

Subproblem 1
w + -1 = 0.845154255

Simplifying
w + -1 = 0.845154255

Reorder the terms:
-1 + w = 0.845154255

Solving
-1 + w = 0.845154255

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 0.845154255 + 1

Combine like terms: -1 + 1 = 0
0 + w = 0.845154255 + 1
w = 0.845154255 + 1

Combine like terms: 0.845154255 + 1 = 1.845154255
w = 1.845154255

Simplifying
w = 1.845154255

Subproblem 2
w + -1 = -0.845154255

Simplifying
w + -1 = -0.845154255

Reorder the terms:
-1 + w = -0.845154255

Solving
-1 + w = -0.845154255

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -0.845154255 + 1

Combine like terms: -1 + 1 = 0
0 + w = -0.845154255 + 1
w = -0.845154255 + 1

Combine like terms: -0.845154255 + 1 = 0.154845745
w = 0.154845745

Simplifying
w = 0.154845745

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.845154255, 0.154845745}