-3q^2-36q=-33

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Solution for -3q^2-36q=-33 equation: 


Simplifying
-3q2 + -36q = -33

Reorder the terms:
-36q + -3q2 = -33

Solving
-36q + -3q2 = -33

Solving for variable 'q'.

Reorder the terms:
33 + -36q + -3q2 = -33 + 33

Combine like terms: -33 + 33 = 0
33 + -36q + -3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -12q + -1q2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(11 + -12q + -1q2)' equal to zero and attempt to solve:

Simplifying
11 + -12q + -1q2 = 0

Solving
11 + -12q + -1q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-11 + 12q + q2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 12q + 11 + q2 = 0 + 11

Reorder the terms:
-11 + 11 + 12q + q2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 12q + q2 = 0 + 11
12q + q2 = 0 + 11

Combine like terms: 0 + 11 = 11
12q + q2 = 11

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 = 11 + 36

Reorder the terms:
36 + 12q + q2 = 11 + 36

Combine like terms: 11 + 36 = 47
36 + 12q + q2 = 47

Factor a perfect square on the left side:
(q + 6)(q + 6) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(q + 6) equal to 6.8556546 and -6.8556546.


Subproblem 1
q + 6 = 6.8556546

Simplifying
q + 6 = 6.8556546

Reorder the terms:
6 + q = 6.8556546

Solving
6 + q = 6.8556546

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 = 6.8556546 + -6

Combine like terms: 6 + -6 = 0
0 + q = 6.8556546 + -6
q = 6.8556546 + -6

Combine like terms: 6.8556546 + -6 = 0.8556546
q = 0.8556546

Simplifying
q = 0.8556546


Subproblem 2
q + 6 = -6.8556546

Simplifying
q + 6 = -6.8556546

Reorder the terms:
6 + q = -6.8556546

Solving
6 + q = -6.8556546

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 = -6.8556546 + -6

Combine like terms: 6 + -6 = 0
0 + q = -6.8556546 + -6
q = -6.8556546 + -6

Combine like terms: -6.8556546 + -6 = -12.8556546
q = -12.8556546

Simplifying
q = -12.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.8556546, -12.8556546}
Solution
q = {0.8556546, -12.8556546}

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