A "cost that contains {X}" may be a spell's total cost, an activated ability's cost, a cost to perform a special action, or a cost you're asked to pay as part of the resolution of a spell or ability (such as Condescend). A spell's total cost includes either its mana cost (printed in the upper right corner) or its alternative cost (such as flashback), as well as any additional costs (such as kicker). If it's something you can spend mana on, it's a cost. If that cost includes the {X} symbol in it, you can spend mana generated by the granted ability on that cost.

You can spend mana generated by the granted ability on any part of a cost that contains {X}. You're not limited to spending it only on the {X} part.

You can spend mana generated by the granted ability on a cost that includes {X} even if you've chosen an X of 0, or if the card specifies that you can spend only colored mana on X. (You'll have to spend the {C}{C} on a different part of that cost, of course.)

You don't have to spend all of the mana on the same cost.