-.2x^2+120x-10000=0

Solution for -.2x^2+120x-10000=0 equation:

Simplifying
-0.2x2 + 120x + -10000 = 0

Reorder the terms:
-10000 + 120x + -0.2x2 = 0

Solving
-10000 + 120x + -0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
50000 + -600x + x2 = 0

Move the constant term to the right:

Add '-50000' to each side of the equation.
50000 + -600x + -50000 + x2 = 0 + -50000

Reorder the terms:
50000 + -50000 + -600x + x2 = 0 + -50000

Combine like terms: 50000 + -50000 = 0
0 + -600x + x2 = 0 + -50000
-600x + x2 = 0 + -50000

Combine like terms: 0 + -50000 = -50000
-600x + x2 = -50000

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 = -50000 + 90000

Reorder the terms:
90000 + -600x + x2 = -50000 + 90000

Combine like terms: -50000 + 90000 = 40000
90000 + -600x + x2 = 40000

Factor a perfect square on the left side:
(x + -300)(x + -300) = 40000

Calculate the square root of the right side: 200

Break this problem into two subproblems by setting 
(x + -300) equal to 200 and -200.

Subproblem 1
x + -300 = 200

Simplifying
x + -300 = 200

Reorder the terms:
-300 + x = 200

Solving
-300 + x = 200

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 = 200 + 300

Combine like terms: -300 + 300 = 0
0 + x = 200 + 300
x = 200 + 300

Combine like terms: 200 + 300 = 500
x = 500

Simplifying
x = 500

Subproblem 2
x + -300 = -200

Simplifying
x + -300 = -200

Reorder the terms:
-300 + x = -200

Solving
-300 + x = -200

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 = -200 + 300

Combine like terms: -300 + 300 = 0
0 + x = -200 + 300
x = -200 + 300

Combine like terms: -200 + 300 = 100
x = 100

Simplifying
x = 100

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {500, 100}