10-0.2q+0.000003q^2=0

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Solution for 10-0.2q+0.000003q^2=0 equation: 


Simplifying
10 + -0.2q + 0.000003q2 = 0

Solving
10 + -0.2q + 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 + -66666.66667q + q2 = 0

Move the constant term to the right:

Add '-3333333.333' to each side of the equation.
3333333.333 + -66666.66667q + -3333333.333 + q2 = 0 + -3333333.333

Reorder the terms:
3333333.333 + -3333333.333 + -66666.66667q + q2 = 0 + -3333333.333

Combine like terms: 3333333.333 + -3333333.333 = 0.000
0.000 + -66666.66667q + q2 = 0 + -3333333.333
-66666.66667q + q2 = 0 + -3333333.333

Combine like terms: 0 + -3333333.333 = -3333333.333
-66666.66667q + q2 = -3333333.333

The q term is -66666.66667q.  Take half its coefficient (-33333.33334).
Square it (1111111112) and add it to both sides.

Add '1111111112' to each side of the equation.
-66666.66667q + 1111111112 + q2 = -3333333.333 + 1111111112

Reorder the terms:
1111111112 + -66666.66667q + q2 = -3333333.333 + 1111111112

Combine like terms: -3333333.333 + 1111111112 = 1107777778.667
1111111112 + -66666.66667q + q2 = 1107777778.667

Factor a perfect square on the left side:
(q + -33333.33334)(q + -33333.33334) = 1107777778.667

Calculate the square root of the right side: 33283.295790336

Break this problem into two subproblems by setting 
(q + -33333.33334) equal to 33283.295790336 and -33283.295790336.


Subproblem 1
q + -33333.33334 = 33283.295790336

Simplifying
q + -33333.33334 = 33283.295790336

Reorder the terms:
-33333.33334 + q = 33283.295790336

Solving
-33333.33334 + q = 33283.295790336

Solving for variable 'q'.

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

Add '33333.33334' to each side of the equation.
-33333.33334 + 33333.33334 + q = 33283.295790336 + 33333.33334

Combine like terms: -33333.33334 + 33333.33334 = 0.00000
0.00000 + q = 33283.295790336 + 33333.33334
q = 33283.295790336 + 33333.33334

Combine like terms: 33283.295790336 + 33333.33334 = 66616.629130336
q = 66616.629130336

Simplifying
q = 66616.629130336


Subproblem 2
q + -33333.33334 = -33283.295790336

Simplifying
q + -33333.33334 = -33283.295790336

Reorder the terms:
-33333.33334 + q = -33283.295790336

Solving
-33333.33334 + q = -33283.295790336

Solving for variable 'q'.

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

Add '33333.33334' to each side of the equation.
-33333.33334 + 33333.33334 + q = -33283.295790336 + 33333.33334

Combine like terms: -33333.33334 + 33333.33334 = 0.00000
0.00000 + q = -33283.295790336 + 33333.33334
q = -33283.295790336 + 33333.33334

Combine like terms: -33283.295790336 + 33333.33334 = 50.037549664
q = 50.037549664

Simplifying
q = 50.037549664


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {66616.629130336, 50.037549664}

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