eli5 why do perfectly inelastic collisions not conserve energy even though we use the same formula for elastic collisons

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Since we use the same exact formula for perfectly inelastic collisions (in which 2 particles stick together after collision) and perfectly elastic ones. Why does one of them conserve energy and the other not.

There is no coefficient of restitution either to quantify the energy losses.

Edit: I know that all energy is conserved in the big picture,, I’m talking about the particles’ energy.

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