x^2=20x-99

Solution for x^2=20x-99 equation:

Simplifying
x2 = 20x + -99

Reorder the terms:
x2 = -99 + 20x

Solving
x2 = -99 + 20x

Solving for variable 'x'.

Reorder the terms:
99 + -20x + x2 = -99 + 20x + 99 + -20x

Reorder the terms:
99 + -20x + x2 = -99 + 99 + 20x + -20x

Combine like terms: -99 + 99 = 0
99 + -20x + x2 = 0 + 20x + -20x
99 + -20x + x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
99 + -20x + x2 = 0

Factor a trinomial.
(9 + -1x)(11 + -1x) = 0

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {9, 11}