-x^2+600x-20000=0

Solution for -x^2+600x-20000=0 equation:

Simplifying
-1x2 + 600x + -20000 = 0

Reorder the terms:
-20000 + 600x + -1x2 = 0

Solving
-20000 + 600x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
20000 + -600x + x2 = 0

Move the constant term to the right:

Add '-20000' to each side of the equation.
20000 + -600x + -20000 + x2 = 0 + -20000

Reorder the terms:
20000 + -20000 + -600x + x2 = 0 + -20000

Combine like terms: 20000 + -20000 = 0
0 + -600x + x2 = 0 + -20000
-600x + x2 = 0 + -20000

Combine like terms: 0 + -20000 = -20000
-600x + x2 = -20000

The x term is -600x.  Take half its coefficient (-300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
-600x + 90000 + x2 = -20000 + 90000

Reorder the terms:
90000 + -600x + x2 = -20000 + 90000

Combine like terms: -20000 + 90000 = 70000
90000 + -600x + x2 = 70000

Factor a perfect square on the left side:
(x + -300)(x + -300) = 70000

Calculate the square root of the right side: 264.575131106

Break this problem into two subproblems by setting 
(x + -300) equal to 264.575131106 and -264.575131106.

Subproblem 1
x + -300 = 264.575131106

Simplifying
x + -300 = 264.575131106

Reorder the terms:
-300 + x = 264.575131106

Solving
-300 + x = 264.575131106

Solving for variable 'x'.

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

Add '300' to each side of the equation.
-300 + 300 + x = 264.575131106 + 300

Combine like terms: -300 + 300 = 0
0 + x = 264.575131106 + 300
x = 264.575131106 + 300

Combine like terms: 264.575131106 + 300 = 564.575131106
x = 564.575131106

Simplifying
x = 564.575131106

Subproblem 2
x + -300 = -264.575131106

Simplifying
x + -300 = -264.575131106

Reorder the terms:
-300 + x = -264.575131106

Solving
-300 + x = -264.575131106

Solving for variable 'x'.

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

Add '300' to each side of the equation.
-300 + 300 + x = -264.575131106 + 300

Combine like terms: -300 + 300 = 0
0 + x = -264.575131106 + 300
x = -264.575131106 + 300

Combine like terms: -264.575131106 + 300 = 35.424868894
x = 35.424868894

Simplifying
x = 35.424868894

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {564.575131106, 35.424868894}