590-12q-0.012q^2=0

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Solution for 590-12q-0.012q^2=0 equation: 


Simplifying
590 + -12q + -0.012q2 = 0

Solving
590 + -12q + -0.012q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
-0.012 the coefficient of the squared term: 

Divide each side by '-0.012'.
-49166.66667 + 1000q + q2 = 0

Move the constant term to the right:

Add '49166.66667' to each side of the equation.
-49166.66667 + 1000q + 49166.66667 + q2 = 0 + 49166.66667

Reorder the terms:
-49166.66667 + 49166.66667 + 1000q + q2 = 0 + 49166.66667

Combine like terms: -49166.66667 + 49166.66667 = 0.00000
0.00000 + 1000q + q2 = 0 + 49166.66667
1000q + q2 = 0 + 49166.66667

Combine like terms: 0 + 49166.66667 = 49166.66667
1000q + q2 = 49166.66667

The q term is 1000q.  Take half its coefficient (500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
1000q + 250000 + q2 = 49166.66667 + 250000

Reorder the terms:
250000 + 1000q + q2 = 49166.66667 + 250000

Combine like terms: 49166.66667 + 250000 = 299166.66667
250000 + 1000q + q2 = 299166.66667

Factor a perfect square on the left side:
(q + 500)(q + 500) = 299166.66667

Calculate the square root of the right side: 546.961302717

Break this problem into two subproblems by setting 
(q + 500) equal to 546.961302717 and -546.961302717.


Subproblem 1
q + 500 = 546.961302717

Simplifying
q + 500 = 546.961302717

Reorder the terms:
500 + q = 546.961302717

Solving
500 + q = 546.961302717

Solving for variable 'q'.

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

Add '-500' to each side of the equation.
500 + -500 + q = 546.961302717 + -500

Combine like terms: 500 + -500 = 0
0 + q = 546.961302717 + -500
q = 546.961302717 + -500

Combine like terms: 546.961302717 + -500 = 46.961302717
q = 46.961302717

Simplifying
q = 46.961302717


Subproblem 2
q + 500 = -546.961302717

Simplifying
q + 500 = -546.961302717

Reorder the terms:
500 + q = -546.961302717

Solving
500 + q = -546.961302717

Solving for variable 'q'.

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

Add '-500' to each side of the equation.
500 + -500 + q = -546.961302717 + -500

Combine like terms: 500 + -500 = 0
0 + q = -546.961302717 + -500
q = -546.961302717 + -500

Combine like terms: -546.961302717 + -500 = -1046.961302717
q = -1046.961302717

Simplifying
q = -1046.961302717


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {46.961302717, -1046.961302717}

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