0=.0001x^2+.05x-2.5

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Solution for 0=.0001x^2+.05x-2.5 equation:


Simplifying
0 = 0.0001x2 + 0.05x + -2.5

Reorder the terms:
0 = -2.5 + 0.05x + 0.0001x2

Solving
0 = -2.5 + 0.05x + 0.0001x2

Solving for variable 'x'.

Combine like terms: 0 + 2.5 = 2.5
2.5 + -0.05x + -0.0001x2 = -2.5 + 0.05x + 0.0001x2 + 2.5 + -0.05x + -0.0001x2

Reorder the terms:
2.5 + -0.05x + -0.0001x2 = -2.5 + 2.5 + 0.05x + -0.05x + 0.0001x2 + -0.0001x2

Combine like terms: -2.5 + 2.5 = 0.0
2.5 + -0.05x + -0.0001x2 = 0.0 + 0.05x + -0.05x + 0.0001x2 + -0.0001x2
2.5 + -0.05x + -0.0001x2 = 0.05x + -0.05x + 0.0001x2 + -0.0001x2

Combine like terms: 0.05x + -0.05x = 0.00
2.5 + -0.05x + -0.0001x2 = 0.00 + 0.0001x2 + -0.0001x2
2.5 + -0.05x + -0.0001x2 = 0.0001x2 + -0.0001x2

Combine like terms: 0.0001x2 + -0.0001x2 = 0.0000
2.5 + -0.05x + -0.0001x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.0001 the coefficient of the squared term: 

Divide each side by '-0.0001'.
-25000 + 500x + x2 = 0

Move the constant term to the right:

Add '25000' to each side of the equation.
-25000 + 500x + 25000 + x2 = 0 + 25000

Reorder the terms:
-25000 + 25000 + 500x + x2 = 0 + 25000

Combine like terms: -25000 + 25000 = 0
0 + 500x + x2 = 0 + 25000
500x + x2 = 0 + 25000

Combine like terms: 0 + 25000 = 25000
500x + x2 = 25000

The x term is 500x.  Take half its coefficient (250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
500x + 62500 + x2 = 25000 + 62500

Reorder the terms:
62500 + 500x + x2 = 25000 + 62500

Combine like terms: 25000 + 62500 = 87500
62500 + 500x + x2 = 87500

Factor a perfect square on the left side:
(x + 250)(x + 250) = 87500

Calculate the square root of the right side: 295.803989155

Break this problem into two subproblems by setting 
(x + 250) equal to 295.803989155 and -295.803989155.

Subproblem 1

x + 250 = 295.803989155 Simplifying x + 250 = 295.803989155 Reorder the terms: 250 + x = 295.803989155 Solving 250 + x = 295.803989155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 295.803989155 + -250 Combine like terms: 250 + -250 = 0 0 + x = 295.803989155 + -250 x = 295.803989155 + -250 Combine like terms: 295.803989155 + -250 = 45.803989155 x = 45.803989155 Simplifying x = 45.803989155

Subproblem 2

x + 250 = -295.803989155 Simplifying x + 250 = -295.803989155 Reorder the terms: 250 + x = -295.803989155 Solving 250 + x = -295.803989155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -295.803989155 + -250 Combine like terms: 250 + -250 = 0 0 + x = -295.803989155 + -250 x = -295.803989155 + -250 Combine like terms: -295.803989155 + -250 = -545.803989155 x = -545.803989155 Simplifying x = -545.803989155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {45.803989155, -545.803989155}

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