w^2+12w=1

Solution for w^2+12w=1 equation:

Simplifying
w2 + 12w = 1

Reorder the terms:
12w + w2 = 1

Solving
12w + w2 = 1

Solving for variable 'w'.

Reorder the terms:
-1 + 12w + w2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 12w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 12w + 1 + w2 = 0 + 1

Reorder the terms:
-1 + 1 + 12w + w2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 12w + w2 = 0 + 1
12w + w2 = 0 + 1

Combine like terms: 0 + 1 = 1
12w + w2 = 1

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 = 1 + 36

Reorder the terms:
36 + 12w + w2 = 1 + 36

Combine like terms: 1 + 36 = 37
36 + 12w + w2 = 37

Factor a perfect square on the left side:
(w + 6)(w + 6) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(w + 6) equal to 6.08276253 and -6.08276253.

Subproblem 1
w + 6 = 6.08276253

Simplifying
w + 6 = 6.08276253

Reorder the terms:
6 + w = 6.08276253

Solving
6 + w = 6.08276253

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 = 6.08276253 + -6

Combine like terms: 6 + -6 = 0
0 + w = 6.08276253 + -6
w = 6.08276253 + -6

Combine like terms: 6.08276253 + -6 = 0.08276253
w = 0.08276253

Simplifying
w = 0.08276253

Subproblem 2
w + 6 = -6.08276253

Simplifying
w + 6 = -6.08276253

Reorder the terms:
6 + w = -6.08276253

Solving
6 + w = -6.08276253

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 = -6.08276253 + -6

Combine like terms: 6 + -6 = 0
0 + w = -6.08276253 + -6
w = -6.08276253 + -6

Combine like terms: -6.08276253 + -6 = -12.08276253
w = -12.08276253

Simplifying
w = -12.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.08276253, -12.08276253}