2x^2-22x+61=1

Solution for 2x^2-22x+61=1 equation:

Simplifying
2x2 + -22x + 61 = 1

Reorder the terms:
61 + -22x + 2x2 = 1

Solving
61 + -22x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
61 + -1 + -22x + 2x2 = 1 + -1

Combine like terms: 61 + -1 = 60
60 + -22x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
60 + -22x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -11x + x2) = 0

Factor a trinomial.
2((5 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {5, 6}