The cost of X can be modified (RRG, p. 23): The letter “X”: ... For costs involving the letter X, the value of X is defined by card ability or player choice, after which the amount paid may be modified by effects without altering the value of X.
The exact mechanism (and detailed explanation) is that when you initiate an ability (i.e., play the "cost X" event), you do the following, in order (RRG, p. 10):
- Check play restrictions
- Determine the cost
- Apply any modifiers to the cost(s).
- Pay the cost(s).
- Choose target(s), if applicable.
- The effects of the ability attempt to initiate.
- The effects of the ability resolve.
So you define X in #2, then modify it (e.g., Paxter) in #3.