25x-x^2=100

Solution for 25x-x^2=100 equation:

Simplifying
25x + -1x2 = 100

Solving
25x + -1x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 25x + -1x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 25x + -1x2 = 0

Factor a trinomial.
(-20 + x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {20, 5}