Complete and balance the following chemical equation: Fe²⁺ + MnO₄⁻ + H⁺ →

The incomplete, unbalanced chemical equation is:
Fe²⁺ + MnO₄⁻ + H⁺ →
The complete, unbalanced chemical equation is:
Fe²⁺ + MnO₄⁻ + H⁺ → Fe³⁺ + Mn²⁺ + H₂O
Fe atoms and Mn atoms are balanced.
The oxidation number of iron increases from +2 (in Fe²⁺) to +3 (in Fe³⁺). Total increase in oxidation number for iron is 3 - 2 = 1.
The oxidation number of Mn decreases from +7 (in MnO₄⁻) to +2 (in Mn²⁺). Total decrease in oxidation number for Mn is 7 - 2 = 5.
To balance total increase in oxidation number with total decrease in oxidation number, add coefficient 5 to iron species.
5Fe²⁺ + MnO₄⁻ + H⁺ → 5Fe³⁺ + Mn²⁺ + H₂O
Balance O atoms by adding 4 water molecules to the products side.
5Fe²⁺ + MnO₄⁻ + H⁺ → 5Fe³⁺ + Mn²⁺ + 4H₂O
Balance H atoms by adding 8 protons to the reactants side.
5Fe²⁺ + MnO₄⁻ + 8H⁺ → 5Fe³⁺ + Mn²⁺ + 4H₂O
This is the complete, balanced chemical equation.