Quick tip: Don't completely peel away the plastic from the base of the phone. The plastic has a mechanical (but not electrical) purpose and should not be removed. The step directions make it seem that you can peel away the plastic, but don't do that. Peel and pry the battery out but leave the plastic in place. I made this mistake and Apple wouldn't repair my iPhone because the plastic was missing. The guy said that the plastic holds the circuitry in place and away from the battery. Do not remove the plastic.
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