w^2+12w+9=0

Solution for w^2+12w+9=0 equation:

Simplifying
w2 + 12w + 9 = 0

Reorder the terms:
9 + 12w + w2 = 0

Solving
9 + 12w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 12w + -9 + w2 = 0 + -9

Reorder the terms:
9 + -9 + 12w + w2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 12w + w2 = 0 + -9
12w + w2 = 0 + -9

Combine like terms: 0 + -9 = -9
12w + w2 = -9

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 = -9 + 36

Reorder the terms:
36 + 12w + w2 = -9 + 36

Combine like terms: -9 + 36 = 27
36 + 12w + w2 = 27

Factor a perfect square on the left side:
(w + 6)(w + 6) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(w + 6) equal to 5.196152423 and -5.196152423.

Subproblem 1
w + 6 = 5.196152423

Simplifying
w + 6 = 5.196152423

Reorder the terms:
6 + w = 5.196152423

Solving
6 + w = 5.196152423

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 = 5.196152423 + -6

Combine like terms: 6 + -6 = 0
0 + w = 5.196152423 + -6
w = 5.196152423 + -6

Combine like terms: 5.196152423 + -6 = -0.803847577
w = -0.803847577

Simplifying
w = -0.803847577

Subproblem 2
w + 6 = -5.196152423

Simplifying
w + 6 = -5.196152423

Reorder the terms:
6 + w = -5.196152423

Solving
6 + w = -5.196152423

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 = -5.196152423 + -6

Combine like terms: 6 + -6 = 0
0 + w = -5.196152423 + -6
w = -5.196152423 + -6

Combine like terms: -5.196152423 + -6 = -11.196152423
w = -11.196152423

Simplifying
w = -11.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.803847577, -11.196152423}