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What does the X in a spell's cost do? For example, Strength of the Tajuru has X in its cost. What do I need to do in order to cast that spell, and what happens with the X when it resolves?
Note: If you need help understanding multikicker, see How does multikicker work?
When you cast a spell with X in its cost, you decide how much X will be and then add that amount to the rest of the spell's cost when you pay it. When the spell resolves, you treat any "X" in the text box of the card as the chosen number.
In the specific case of Strength of the Tajuru, you choose a number for X, then (assuming you don't kick it) you pay the chosen number mana of any color, plus 2 green mana. When the spell resolves, you add the chosen number of counters to the target creature.
The basic rulebook has a description of X costs in the glossary:
X, {X}—Some spells and abilities have effects that change depending on how much mana you use to pay for them. For example, Heat Ray is an instant spell that costs {X}{R} and deals X damage. If you paid {3}{R} to cast it, it would deal 3 damage. If you paid {6}{R} to cast it, it would deal 6 damage.
Rule 601.2b more specifically covers paying for spells with X costs:
If the spell is modal the player announces the mode choice (see rule 700.2). If the player wishes to splice any cards onto the spell (see rule 702.46), he or she reveals those cards in his or her hand. If the spell has alternative or additional costs that will be paid as it's being cast such as buyback or kicker costs (see rules 117.8 and 117.9), the player announces his or her intentions to pay any or all of those costs (see rule 601.2e). A player can't apply two alternative methods of casting or two alternative costs to a single spell. If the spell has a variable cost that will be paid as it's being cast (such as an {X} in its mana cost; see rule 107.3), the player announces the value of that variable. If a cost that will be paid as the spell is being cast includes hybrid mana symbols, the player announces the nonhybrid equivalent cost he or she intends to pay. If a cost that will be paid as the spell is being cast includes Phyrexian mana symbols, the player announces whether he or she intends to pay 2 life or the corresponding colored mana cost for each of those symbols. Previously made choices (such as choosing to cast a spell with flashback from a graveyard or choosing to cast a creature with morph face down) may restrict the player's options when making these choices.
When a card with {X} in its cost is in any zone other than the stack, the X is considered to be 0 for the purpose of any calculations. This is specified in rule 202.3b:
When calculating the converted mana cost of an object with an Manax.gif in its mana cost, X is treated as 0 while the object is not on the stack, and X is treated as the number chosen for it while the object is on the stack
The one exception is permanents' abilities that need to know about their own mana costs, as rule 400.7c says:
If an ability of a permanent requires information about choices made as that permanent was cast as a spell, including what mana was spent to cast that spell, it uses information about the spell that became that permanent as it resolved.
A cost that includes {X} is a variable cost, you can pick any value for {X} that you want and that number is used to determine the effect of the spell, exactly what the variable does is dependent on the text of the spell. For example, Blaze has a cost of {X}{R} and rules text that says Blaze deals X damage to target creature or player. so what you do when you cast it is determine how much damage you want to do, this number will be {X}, so if you want to deal 3 damage to your opponent Blaze will cost {3}{R}.
Some cards have costs that are {X}{X} like Chalice of the Void, the way this works is you pick the value you want for X and then pay that twice, so if you want the Chalice to have 2 counters on it you would have to pay {2}{2} or {4} total. Astral Cornucopia is similar with its {X}{X}{X} cost but you pay three times X.
For cards with {X} in their cost the {X} is assumed to be zero anytime a card cares about its Converted Mana Cost except for when it is on the stack and you have actually payed mana for it. So if you have an Izzet Guildmage you can use its ability to copy sorceries with a CMC of 2 or less on Blaze only if X is 1 (or 0 but why would you cast it then?). However if you have a Primordial Hydra that you paid {10}{G}{G} for it could still be destroyed by an Abrupt Decay because on the battlefield its CMC is only 2.
Because the {X} is 0 unless you pay mana to cast it this also means that while you can cast them off of effects that allow you to play spell without paying their mana cost like Omniscience you have to pick {0} for X, there is no way to cast Blaze with Omniscience and have it deal damage.
