(-2.5x^2)+500x+20000=0

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Solution for (-2.5x^2)+500x+20000=0 equation:


Simplifying
(-2.5x2) + 500x + 20000 = 0

Reorder the terms:
20000 + 500x + (-2.5x2) = 0

Solving
20000 + 500x + (-2.5x2) = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.5 the coefficient of the squared term: 

Divide each side by '-2.5'.
-8000 + -200x + x2 = 0

Move the constant term to the right:

Add '8000' to each side of the equation.
-8000 + -200x + 8000 + x2 = 0 + 8000

Reorder the terms:
-8000 + 8000 + -200x + x2 = 0 + 8000

Combine like terms: -8000 + 8000 = 0
0 + -200x + x2 = 0 + 8000
-200x + x2 = 0 + 8000

Combine like terms: 0 + 8000 = 8000
-200x + x2 = 8000

The x term is -200x.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200x + 10000 + x2 = 8000 + 10000

Reorder the terms:
10000 + -200x + x2 = 8000 + 10000

Combine like terms: 8000 + 10000 = 18000
10000 + -200x + x2 = 18000

Factor a perfect square on the left side:
((x) + -100)((x) + -100) = 18000

Calculate the square root of the right side: 134.16407865

Break this problem into two subproblems by setting 
((x) + -100) equal to 134.16407865 and -134.16407865.

Subproblem 1

(x) + -100 = 134.16407865 Simplifying (x) + -100 = 134.16407865 x + -100 = 134.16407865 Reorder the terms: -100 + x = 134.16407865 Solving -100 + x = 134.16407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 134.16407865 + 100 Combine like terms: -100 + 100 = 0 0 + x = 134.16407865 + 100 x = 134.16407865 + 100 Combine like terms: 134.16407865 + 100 = 234.16407865 x = 234.16407865 Simplifying x = 234.16407865

Subproblem 2

(x) + -100 = -134.16407865 Simplifying (x) + -100 = -134.16407865 x + -100 = -134.16407865 Reorder the terms: -100 + x = -134.16407865 Solving -100 + x = -134.16407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -134.16407865 + 100 Combine like terms: -100 + 100 = 0 0 + x = -134.16407865 + 100 x = -134.16407865 + 100 Combine like terms: -134.16407865 + 100 = -34.16407865 x = -34.16407865 Simplifying x = -34.16407865

Solution

The solution to the problem is based on the solutions from the subproblems. x = {234.16407865, -34.16407865}

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