q^2+12q+5=0

Solution for q^2+12q+5=0 equation:

Simplifying
q2 + 12q + 5 = 0

Reorder the terms:
5 + 12q + q2 = 0

Solving
5 + 12q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 12q + -5 + q2 = 0 + -5

Reorder the terms:
5 + -5 + 12q + q2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 12q + q2 = 0 + -5
12q + q2 = 0 + -5

Combine like terms: 0 + -5 = -5
12q + q2 = -5

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

Add '36' to each side of the equation.
12q + 36 + q2 = -5 + 36

Reorder the terms:
36 + 12q + q2 = -5 + 36

Combine like terms: -5 + 36 = 31
36 + 12q + q2 = 31

Factor a perfect square on the left side:
(q + 6)(q + 6) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(q + 6) equal to 5.567764363 and -5.567764363.

Subproblem 1
q + 6 = 5.567764363

Simplifying
q + 6 = 5.567764363

Reorder the terms:
6 + q = 5.567764363

Solving
6 + q = 5.567764363

Solving for variable 'q'.

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

Add '-6' to each side of the equation.
6 + -6 + q = 5.567764363 + -6

Combine like terms: 6 + -6 = 0
0 + q = 5.567764363 + -6
q = 5.567764363 + -6

Combine like terms: 5.567764363 + -6 = -0.432235637
q = -0.432235637

Simplifying
q = -0.432235637

Subproblem 2
q + 6 = -5.567764363

Simplifying
q + 6 = -5.567764363

Reorder the terms:
6 + q = -5.567764363

Solving
6 + q = -5.567764363

Solving for variable 'q'.

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

Add '-6' to each side of the equation.
6 + -6 + q = -5.567764363 + -6

Combine like terms: 6 + -6 = 0
0 + q = -5.567764363 + -6
q = -5.567764363 + -6

Combine like terms: -5.567764363 + -6 = -11.567764363
q = -11.567764363

Simplifying
q = -11.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-0.432235637, -11.567764363}