0=w^2-7w-6

Solution for 0=w^2-7w-6 equation:

Simplifying
0 = w2 + -7w + -6

Reorder the terms:
0 = -6 + -7w + w2

Solving
0 = -6 + -7w + w2

Solving for variable 'w'.

Combine like terms: 0 + 6 = 6
6 + 7w + -1w2 = -6 + -7w + w2 + 6 + 7w + -1w2

Reorder the terms:
6 + 7w + -1w2 = -6 + 6 + -7w + 7w + w2 + -1w2

Combine like terms: -6 + 6 = 0
6 + 7w + -1w2 = 0 + -7w + 7w + w2 + -1w2
6 + 7w + -1w2 = -7w + 7w + w2 + -1w2

Combine like terms: -7w + 7w = 0
6 + 7w + -1w2 = 0 + w2 + -1w2
6 + 7w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
6 + 7w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -7w + w2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -7w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + -7w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7w + w2 = 0 + 6
-7w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
-7w + w2 = 6

The w term is -7w.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7w + 12.25 + w2 = 6 + 12.25

Reorder the terms:
12.25 + -7w + w2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + -7w + w2 = 18.25

Factor a perfect square on the left side:
(w + -3.5)(w + -3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(w + -3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
w + -3.5 = 4.272001873

Simplifying
w + -3.5 = 4.272001873

Reorder the terms:
-3.5 + w = 4.272001873

Solving
-3.5 + w = 4.272001873

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = 4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = 4.272001873 + 3.5
w = 4.272001873 + 3.5

Combine like terms: 4.272001873 + 3.5 = 7.772001873
w = 7.772001873

Simplifying
w = 7.772001873

Subproblem 2
w + -3.5 = -4.272001873

Simplifying
w + -3.5 = -4.272001873

Reorder the terms:
-3.5 + w = -4.272001873

Solving
-3.5 + w = -4.272001873

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = -4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = -4.272001873 + 3.5
w = -4.272001873 + 3.5

Combine like terms: -4.272001873 + 3.5 = -0.772001873
w = -0.772001873

Simplifying
w = -0.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.772001873, -0.772001873}