x^2-10x+22=1

Solution for x^2-10x+22=1 equation:

Simplifying
x2 + -10x + 22 = 1

Reorder the terms:
22 + -10x + x2 = 1

Solving
22 + -10x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
22 + -1 + -10x + x2 = 1 + -1

Combine like terms: 22 + -1 = 21
21 + -10x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
21 + -10x + x2 = 0

Factor a trinomial.
(3 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {3, 7}