10-0.02q+0.000003q^2=0

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Solution for 10-0.02q+0.000003q^2=0 equation: 


Simplifying
10 + -0.02q + 0.000003q2 = 0

Solving
10 + -0.02q + 0.000003q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
0.000003 the coefficient of the squared term: 

Divide each side by '0.000003'.
3333333.333 + -6666.666667q + q2 = 0

Move the constant term to the right:

Add '-3333333.333' to each side of the equation.
3333333.333 + -6666.666667q + -3333333.333 + q2 = 0 + -3333333.333

Reorder the terms:
3333333.333 + -3333333.333 + -6666.666667q + q2 = 0 + -3333333.333

Combine like terms: 3333333.333 + -3333333.333 = 0.000
0.000 + -6666.666667q + q2 = 0 + -3333333.333
-6666.666667q + q2 = 0 + -3333333.333

Combine like terms: 0 + -3333333.333 = -3333333.333
-6666.666667q + q2 = -3333333.333

The q term is -6666.666667q.  Take half its coefficient (-3333.333334).
Square it (11111111.12) and add it to both sides.

Add '11111111.12' to each side of the equation.
-6666.666667q + 11111111.12 + q2 = -3333333.333 + 11111111.12

Reorder the terms:
11111111.12 + -6666.666667q + q2 = -3333333.333 + 11111111.12

Combine like terms: -3333333.333 + 11111111.12 = 7777777.787
11111111.12 + -6666.666667q + q2 = 7777777.787

Factor a perfect square on the left side:
(q + -3333.333334)(q + -3333.333334) = 7777777.787

Calculate the square root of the right side: 2788.866756767

Break this problem into two subproblems by setting 
(q + -3333.333334) equal to 2788.866756767 and -2788.866756767.


Subproblem 1
q + -3333.333334 = 2788.866756767

Simplifying
q + -3333.333334 = 2788.866756767

Reorder the terms:
-3333.333334 + q = 2788.866756767

Solving
-3333.333334 + q = 2788.866756767

Solving for variable 'q'.

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

Add '3333.333334' to each side of the equation.
-3333.333334 + 3333.333334 + q = 2788.866756767 + 3333.333334

Combine like terms: -3333.333334 + 3333.333334 = 0.000000
0.000000 + q = 2788.866756767 + 3333.333334
q = 2788.866756767 + 3333.333334

Combine like terms: 2788.866756767 + 3333.333334 = 6122.200090767
q = 6122.200090767

Simplifying
q = 6122.200090767


Subproblem 2
q + -3333.333334 = -2788.866756767

Simplifying
q + -3333.333334 = -2788.866756767

Reorder the terms:
-3333.333334 + q = -2788.866756767

Solving
-3333.333334 + q = -2788.866756767

Solving for variable 'q'.

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

Add '3333.333334' to each side of the equation.
-3333.333334 + 3333.333334 + q = -2788.866756767 + 3333.333334

Combine like terms: -3333.333334 + 3333.333334 = 0.000000
0.000000 + q = -2788.866756767 + 3333.333334
q = -2788.866756767 + 3333.333334

Combine like terms: -2788.866756767 + 3333.333334 = 544.466577233
q = 544.466577233

Simplifying
q = 544.466577233


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {6122.200090767, 544.466577233}

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