.003x^2+.01x-2=0

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Solution for .003x^2+.01x-2=0 equation: 


Simplifying
0.003x2 + 0.01x + -2 = 0

Reorder the terms:
-2 + 0.01x + 0.003x2 = 0

Solving
-2 + 0.01x + 0.003x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.003'.
-666.6666667 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '666.6666667' to each side of the equation.
-666.6666667 + 3.333333333x + 666.6666667 + x2 = 0 + 666.6666667

Reorder the terms:
-666.6666667 + 666.6666667 + 3.333333333x + x2 = 0 + 666.6666667

Combine like terms: -666.6666667 + 666.6666667 = 0.0000000
0.0000000 + 3.333333333x + x2 = 0 + 666.6666667
3.333333333x + x2 = 0 + 666.6666667

Combine like terms: 0 + 666.6666667 = 666.6666667
3.333333333x + x2 = 666.6666667

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 666.6666667 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 666.6666667 + 2.777777779

Combine like terms: 666.6666667 + 2.777777779 = 669.444444479
2.777777779 + 3.333333333x + x2 = 669.444444479

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 669.444444479

Calculate the square root of the right side: 25.873624494

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 25.873624494 and -25.873624494.


Subproblem 1
x + 1.666666667 = 25.873624494

Simplifying
x + 1.666666667 = 25.873624494

Reorder the terms:
1.666666667 + x = 25.873624494

Solving
1.666666667 + x = 25.873624494

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 25.873624494 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 25.873624494 + -1.666666667
x = 25.873624494 + -1.666666667

Combine like terms: 25.873624494 + -1.666666667 = 24.206957827
x = 24.206957827

Simplifying
x = 24.206957827


Subproblem 2
x + 1.666666667 = -25.873624494

Simplifying
x + 1.666666667 = -25.873624494

Reorder the terms:
1.666666667 + x = -25.873624494

Solving
1.666666667 + x = -25.873624494

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -25.873624494 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -25.873624494 + -1.666666667
x = -25.873624494 + -1.666666667

Combine like terms: -25.873624494 + -1.666666667 = -27.540291161
x = -27.540291161

Simplifying
x = -27.540291161


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.206957827, -27.540291161}

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