casting with out paying mana cost

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If you have a spell or an effect that lets you cast another spell without paying its mana cost. am i able to pay into x. ie.
possibility storm is on the field. i cast dissipate. then i exile till i reveal sphinks revelation. am i able to pay into x on the sphinks 

" To each his own."   But my way is probably better

No. When you are casting a spell without paying its mana cost, the only legal choice you can make if there's an X-value involved is zero.

Incidentally, you also appear to misunderstand how X values work in general. X is not determined by what you pay. Rather, first you choose (or at least determine, for cases like Spell Blast) a value for X, then substitute that in for all instances of X on that card, including the one(s) in its cost.

(This actually complicates the answer to this question, though it simplifies the answers to many others - if it worked the way you appear to think, the answer would just be "you're not paying the mana cost, that means just what it says - you can't pay into X". But that's not how it works, so there has to be a separate rule that specifically addresses this situation.)
Jeff Heikkinen DCI Rules Advisor since Dec 25, 2011
107.3b If a player is casting a spell that has an {X} in its mana cost, the value of X isn’t defined by the text of that spell, and an effect lets that player cast that spell while paying neither its mana cost nor an alternative cost that includes X, then the only legal choice for X is 0. This doesn’t apply to effects that only reduce a cost, even if they reduce it to zero.

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