510-12q-0.012q^2=0

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Solution for 510-12q-0.012q^2=0 equation: 


Simplifying
510 + -12q + -0.012q2 = 0

Solving
510 + -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'.
-42500 + 1000q + q2 = 0

Move the constant term to the right:

Add '42500' to each side of the equation.
-42500 + 1000q + 42500 + q2 = 0 + 42500

Reorder the terms:
-42500 + 42500 + 1000q + q2 = 0 + 42500

Combine like terms: -42500 + 42500 = 0
0 + 1000q + q2 = 0 + 42500
1000q + q2 = 0 + 42500

Combine like terms: 0 + 42500 = 42500
1000q + q2 = 42500

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 = 42500 + 250000

Reorder the terms:
250000 + 1000q + q2 = 42500 + 250000

Combine like terms: 42500 + 250000 = 292500
250000 + 1000q + q2 = 292500

Factor a perfect square on the left side:
(q + 500)(q + 500) = 292500

Calculate the square root of the right side: 540.83269132

Break this problem into two subproblems by setting 
(q + 500) equal to 540.83269132 and -540.83269132.


Subproblem 1
q + 500 = 540.83269132

Simplifying
q + 500 = 540.83269132

Reorder the terms:
500 + q = 540.83269132

Solving
500 + q = 540.83269132

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 = 540.83269132 + -500

Combine like terms: 500 + -500 = 0
0 + q = 540.83269132 + -500
q = 540.83269132 + -500

Combine like terms: 540.83269132 + -500 = 40.83269132
q = 40.83269132

Simplifying
q = 40.83269132


Subproblem 2
q + 500 = -540.83269132

Simplifying
q + 500 = -540.83269132

Reorder the terms:
500 + q = -540.83269132

Solving
500 + q = -540.83269132

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 = -540.83269132 + -500

Combine like terms: 500 + -500 = 0
0 + q = -540.83269132 + -500
q = -540.83269132 + -500

Combine like terms: -540.83269132 + -500 = -1040.83269132
q = -1040.83269132

Simplifying
q = -1040.83269132


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {40.83269132, -1040.83269132}

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