X^2-5X+5=1

Solution for X^2-5X+5=1 equation:

Simplifying
X2 + -5X + 5 = 1

Reorder the terms:
5 + -5X + X2 = 1

Solving
5 + -5X + X2 = 1

Solving for variable 'X'.

Reorder the terms:
5 + -1 + -5X + X2 = 1 + -1

Combine like terms: 5 + -1 = 4
4 + -5X + X2 = 1 + -1

Combine like terms: 1 + -1 = 0
4 + -5X + X2 = 0

Factor a trinomial.
(1 + -1X)(4 + -1X) = 0

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

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Subproblem 2
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
Solution
X = {1, 4}