w^2-12w-4=0

Solution for w^2-12w-4=0 equation:

Simplifying
w2 + -12w + -4 = 0

Reorder the terms:
-4 + -12w + w2 = 0

Solving
-4 + -12w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -12w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + -12w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -12w + w2 = 0 + 4
-12w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-12w + w2 = 4

The w term is -12w.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12w + 36 + w2 = 4 + 36

Reorder the terms:
36 + -12w + w2 = 4 + 36

Combine like terms: 4 + 36 = 40
36 + -12w + w2 = 40

Factor a perfect square on the left side:
(w + -6)(w + -6) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(w + -6) equal to 6.32455532 and -6.32455532.

Subproblem 1
w + -6 = 6.32455532

Simplifying
w + -6 = 6.32455532

Reorder the terms:
-6 + w = 6.32455532

Solving
-6 + w = 6.32455532

Solving for variable 'w'.

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

Add '6' to each side of the equation.
-6 + 6 + w = 6.32455532 + 6

Combine like terms: -6 + 6 = 0
0 + w = 6.32455532 + 6
w = 6.32455532 + 6

Combine like terms: 6.32455532 + 6 = 12.32455532
w = 12.32455532

Simplifying
w = 12.32455532

Subproblem 2
w + -6 = -6.32455532

Simplifying
w + -6 = -6.32455532

Reorder the terms:
-6 + w = -6.32455532

Solving
-6 + w = -6.32455532

Solving for variable 'w'.

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

Add '6' to each side of the equation.
-6 + 6 + w = -6.32455532 + 6

Combine like terms: -6 + 6 = 0
0 + w = -6.32455532 + 6
w = -6.32455532 + 6

Combine like terms: -6.32455532 + 6 = -0.32455532
w = -0.32455532

Simplifying
w = -0.32455532

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {12.32455532, -0.32455532}