Wow, the previous owner drove with 51 PSI? That must jar your teeth loose every time you hit a pebble in the road.
I have 265/35/22 tires and I cold inflate mine to 36 PSI. Driving around will heat the tires and increase the tire pressure. The heated tire pressure increases to 38 - 40 PSI ... depending on whether it's high speed interstate or just around town. The brand of tire will make some difference as well. Some brands have a stiffer sidewall and will ride stiffer.
I agree that 32 PSI is too low for the 22" low profile tires. I would start at 36 PSI and increase the pressure to a point where the drive feels firm but not too harsh. I usually look at the contact patch on the tire tread to determine whether to increase/decrease the tire pressure.
Wipe some tire shine (e.g. Armor All) on your sidewall plus and inch or so onto the tread. Drive the car around for a day or so and then look to see how much tire protectant has been removed on the tread. Ideally, you would like the wear pattern to come to the edge of the tread without going over to the sidewall (psi too low). You also don't want the wear pattern too far from the edge towards the center of the tire (psi too high).
Depending on the weight distribution of the car, you may have different PSI for the front vs the rear. Since the Dodge Charger is close to 50/50 I have found that the same PSI all-round works fine for my car.
Reported weight distribution is 53/47 (V6) and 54/46 (V8).
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