x^2-22x+113=1

Solution for x^2-22x+113=1 equation:

Simplifying
x2 + -22x + 113 = 1

Reorder the terms:
113 + -22x + x2 = 1

Solving
113 + -22x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
113 + -1 + -22x + x2 = 1 + -1

Combine like terms: 113 + -1 = 112
112 + -22x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
112 + -22x + x2 = 0

Factor a trinomial.
(8 + -1x)(14 + -1x) = 0

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {8, 14}