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The chemical equation needs to be balanced becasue in the equilibrium equation, each species is raised to the power of its stoichiometric coefficient (which is obtained from the balanced chemical equation).
Though the concentrations don't affect Kc, the coefficients in a balanced equation are needed to calculate the equilibrium constant. You need to raise the concentrations to the power of how many mols are in the reaction.
Using the balanced equation is imperative because the stoichiometric coefficients are needed in order to solve for KC as they are what you raise each concentration to the power of. Therefore you need the correct balanced ratio for each reaction and the stoichiometric coefficients are necessary.
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