-0.002x^2+0.5x-10=0

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Solution for -0.002x^2+0.5x-10=0 equation: 


Simplifying
-0.002x2 + 0.5x + -10 = 0

Reorder the terms:
-10 + 0.5x + -0.002x2 = 0

Solving
-10 + 0.5x + -0.002x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.002 the coefficient of the squared term: 

Divide each side by '-0.002'.
5000 + -250x + x2 = 0

Move the constant term to the right:

Add '-5000' to each side of the equation.
5000 + -250x + -5000 + x2 = 0 + -5000

Reorder the terms:
5000 + -5000 + -250x + x2 = 0 + -5000

Combine like terms: 5000 + -5000 = 0
0 + -250x + x2 = 0 + -5000
-250x + x2 = 0 + -5000

Combine like terms: 0 + -5000 = -5000
-250x + x2 = -5000

The x term is -250x.  Take half its coefficient (-125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
-250x + 15625 + x2 = -5000 + 15625

Reorder the terms:
15625 + -250x + x2 = -5000 + 15625

Combine like terms: -5000 + 15625 = 10625
15625 + -250x + x2 = 10625

Factor a perfect square on the left side:
(x + -125)(x + -125) = 10625

Calculate the square root of the right side: 103.07764064

Break this problem into two subproblems by setting 
(x + -125) equal to 103.07764064 and -103.07764064.


Subproblem 1
x + -125 = 103.07764064

Simplifying
x + -125 = 103.07764064

Reorder the terms:
-125 + x = 103.07764064

Solving
-125 + x = 103.07764064

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = 103.07764064 + 125

Combine like terms: -125 + 125 = 0
0 + x = 103.07764064 + 125
x = 103.07764064 + 125

Combine like terms: 103.07764064 + 125 = 228.07764064
x = 228.07764064

Simplifying
x = 228.07764064


Subproblem 2
x + -125 = -103.07764064

Simplifying
x + -125 = -103.07764064

Reorder the terms:
-125 + x = -103.07764064

Solving
-125 + x = -103.07764064

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = -103.07764064 + 125

Combine like terms: -125 + 125 = 0
0 + x = -103.07764064 + 125
x = -103.07764064 + 125

Combine like terms: -103.07764064 + 125 = 21.92235936
x = 21.92235936

Simplifying
x = 21.92235936


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {228.07764064, 21.92235936}

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