2x^2-18x+41=1

Solution for 2x^2-18x+41=1 equation:

Simplifying
2x2 + -18x + 41 = 1

Reorder the terms:
41 + -18x + 2x2 = 1

Solving
41 + -18x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
41 + -1 + -18x + 2x2 = 1 + -1

Combine like terms: 41 + -1 = 40
40 + -18x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
40 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -9x + x2) = 0

Factor a trinomial.
2((4 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
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
Solution
x = {4, 5}