q^2-400-12q=0

Solution for q^2-400-12q=0 equation:

Simplifying
q2 + -400 + -12q = 0

Reorder the terms:
-400 + -12q + q2 = 0

Solving
-400 + -12q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -12q + 400 + q2 = 0 + 400

Reorder the terms:
-400 + 400 + -12q + q2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -12q + q2 = 0 + 400
-12q + q2 = 0 + 400

Combine like terms: 0 + 400 = 400
-12q + q2 = 400

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 = 400 + 36

Reorder the terms:
36 + -12q + q2 = 400 + 36

Combine like terms: 400 + 36 = 436
36 + -12q + q2 = 436

Factor a perfect square on the left side:
(q + -6)(q + -6) = 436

Calculate the square root of the right side: 20.880613018

Break this problem into two subproblems by setting 
(q + -6) equal to 20.880613018 and -20.880613018.

Subproblem 1
q + -6 = 20.880613018

Simplifying
q + -6 = 20.880613018

Reorder the terms:
-6 + q = 20.880613018

Solving
-6 + q = 20.880613018

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 = 20.880613018 + 6

Combine like terms: -6 + 6 = 0
0 + q = 20.880613018 + 6
q = 20.880613018 + 6

Combine like terms: 20.880613018 + 6 = 26.880613018
q = 26.880613018

Simplifying
q = 26.880613018

Subproblem 2
q + -6 = -20.880613018

Simplifying
q + -6 = -20.880613018

Reorder the terms:
-6 + q = -20.880613018

Solving
-6 + q = -20.880613018

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 = -20.880613018 + 6

Combine like terms: -6 + 6 = 0
0 + q = -20.880613018 + 6
q = -20.880613018 + 6

Combine like terms: -20.880613018 + 6 = -14.880613018
q = -14.880613018

Simplifying
q = -14.880613018

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {26.880613018, -14.880613018}