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Suggestions in other post were good.
A little physics: if you do the theoretical math on a lead acid battery, you find that the full potential for a lead/acid cell is 2.1 volts.
Therefore, a fully-charged battery should read 12.6 volts with no load on it. Anything you read above 12.6 volts with the car turned off is what is known as "surface charge" which is analogous to a charged capacitor. If you turn on the headlights for a few seconds and then turn them off, you will measure the voltage due only to the chemical reaction, or exactly 12.6 volts.
It doesn't sound like you have any cause for concern at this point.
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