q^2-12q-1=0

Solution for q^2-12q-1=0 equation:

Simplifying
q2 + -12q + -1 = 0

Reorder the terms:
-1 + -12q + q2 = 0

Solving
-1 + -12q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -12q + 1 + q2 = 0 + 1

Reorder the terms:
-1 + 1 + -12q + q2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -12q + q2 = 0 + 1
-12q + q2 = 0 + 1

Combine like terms: 0 + 1 = 1
-12q + q2 = 1

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 = 1 + 36

Reorder the terms:
36 + -12q + q2 = 1 + 36

Combine like terms: 1 + 36 = 37
36 + -12q + q2 = 37

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

Calculate the square root of the right side: 6.08276253

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

Subproblem 1
q + -6 = 6.08276253

Simplifying
q + -6 = 6.08276253

Reorder the terms:
-6 + q = 6.08276253

Solving
-6 + q = 6.08276253

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 = 6.08276253 + 6

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

Combine like terms: 6.08276253 + 6 = 12.08276253
q = 12.08276253

Simplifying
q = 12.08276253

Subproblem 2
q + -6 = -6.08276253

Simplifying
q + -6 = -6.08276253

Reorder the terms:
-6 + q = -6.08276253

Solving
-6 + q = -6.08276253

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 = -6.08276253 + 6

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

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

Simplifying
q = -0.08276253

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