200x-x^2=10000

Solution for 200x-x^2=10000 equation:

Simplifying
200x + -1x2 = 10000

Solving
200x + -1x2 = 10000

Solving for variable 'x'.

Reorder the terms:
-10000 + 200x + -1x2 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-10000 + 200x + -1x2 = 0

Factor a trinomial.
(-100 + x)(100 + -1x) = 0

Subproblem 1
Set the factor '(-100 + x)' equal to zero and attempt to solve:

Simplifying
-100 + x = 0

Solving
-100 + x = 0

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 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + x = 0 + 100
x = 0 + 100

Combine like terms: 0 + 100 = 100
x = 100

Simplifying
x = 100
Subproblem 2
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x = 0 + -100
-1x = 0 + -100

Combine like terms: 0 + -100 = -100
-1x = -100

Divide each side by '-1'.
x = 100

Simplifying
x = 100
Solution
x = {100, 100}