91q^2-42q-36=0

Solution for 91q^2-42q-36=0 equation:

Simplifying
91q2 + -42q + -36 = 0

Reorder the terms:
-36 + -42q + 91q2 = 0

Solving
-36 + -42q + 91q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
91 the coefficient of the squared term: 

Divide each side by '91'.
-0.3956043956 + -0.4615384615q + q2 = 0

Move the constant term to the right:

Add '0.3956043956' to each side of the equation.
-0.3956043956 + -0.4615384615q + 0.3956043956 + q2 = 0 + 0.3956043956

Reorder the terms:
-0.3956043956 + 0.3956043956 + -0.4615384615q + q2 = 0 + 0.3956043956

Combine like terms: -0.3956043956 + 0.3956043956 = 0.0000000000
0.0000000000 + -0.4615384615q + q2 = 0 + 0.3956043956
-0.4615384615q + q2 = 0 + 0.3956043956

Combine like terms: 0 + 0.3956043956 = 0.3956043956
-0.4615384615q + q2 = 0.3956043956

The q term is -0.4615384615q.  Take half its coefficient (-0.2307692308).
Square it (0.05325443788) and add it to both sides.

Add '0.05325443788' to each side of the equation.
-0.4615384615q + 0.05325443788 + q2 = 0.3956043956 + 0.05325443788

Reorder the terms:
0.05325443788 + -0.4615384615q + q2 = 0.3956043956 + 0.05325443788

Combine like terms: 0.3956043956 + 0.05325443788 = 0.44885883348
0.05325443788 + -0.4615384615q + q2 = 0.44885883348

Factor a perfect square on the left side:
(q + -0.2307692308)(q + -0.2307692308) = 0.44885883348

Calculate the square root of the right side: 0.669969278

Break this problem into two subproblems by setting 
(q + -0.2307692308) equal to 0.669969278 and -0.669969278.

Subproblem 1
q + -0.2307692308 = 0.669969278

Simplifying
q + -0.2307692308 = 0.669969278

Reorder the terms:
-0.2307692308 + q = 0.669969278

Solving
-0.2307692308 + q = 0.669969278

Solving for variable 'q'.

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

Add '0.2307692308' to each side of the equation.
-0.2307692308 + 0.2307692308 + q = 0.669969278 + 0.2307692308

Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000
0.0000000000 + q = 0.669969278 + 0.2307692308
q = 0.669969278 + 0.2307692308

Combine like terms: 0.669969278 + 0.2307692308 = 0.9007385088
q = 0.9007385088

Simplifying
q = 0.9007385088

Subproblem 2
q + -0.2307692308 = -0.669969278

Simplifying
q + -0.2307692308 = -0.669969278

Reorder the terms:
-0.2307692308 + q = -0.669969278

Solving
-0.2307692308 + q = -0.669969278

Solving for variable 'q'.

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

Add '0.2307692308' to each side of the equation.
-0.2307692308 + 0.2307692308 + q = -0.669969278 + 0.2307692308

Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000
0.0000000000 + q = -0.669969278 + 0.2307692308
q = -0.669969278 + 0.2307692308

Combine like terms: -0.669969278 + 0.2307692308 = -0.4392000472
q = -0.4392000472

Simplifying
q = -0.4392000472

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.9007385088, -0.4392000472}