2275=x(100-x)

Solution for 2275=x(100-x) equation:

Simplifying
2275 = x(100 + -1x)
2275 = (100 * x + -1x * x)
2275 = (100x + -1x2)

Solving
2275 = 100x + -1x2

Solving for variable 'x'.

Reorder the terms:
2275 + -100x + x2 = 100x + -100x + -1x2 + x2

Combine like terms: 100x + -100x = 0
2275 + -100x + x2 = 0 + -1x2 + x2
2275 + -100x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
2275 + -100x + x2 = 0

Factor a trinomial.
(35 + -1x)(65 + -1x) = 0

Subproblem 1
Set the factor '(35 + -1x)' equal to zero and attempt to solve:

Simplifying
35 + -1x = 0

Solving
35 + -1x = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1x = 0 + -35
-1x = 0 + -35

Combine like terms: 0 + -35 = -35
-1x = -35

Divide each side by '-1'.
x = 35

Simplifying
x = 35
Subproblem 2
Set the factor '(65 + -1x)' equal to zero and attempt to solve:

Simplifying
65 + -1x = 0

Solving
65 + -1x = 0

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

Add '-65' to each side of the equation.
65 + -65 + -1x = 0 + -65

Combine like terms: 65 + -65 = 0
0 + -1x = 0 + -65
-1x = 0 + -65

Combine like terms: 0 + -65 = -65
-1x = -65

Divide each side by '-1'.
x = 65

Simplifying
x = 65
Solution
x = {35, 65}