Alright, looking at HP's site, it does have a PCIe 16x slot, and it should support the 750 ti. However, I doubt it can support anything higher as the PSU is only 300W. Yes 300W!Data: PCIe 16x on mobos
Power: Does not require extra connectors, PSU wattage just barely hits minimum requirements
Physical: Hopefully card is short enough, and have 2 slots in the back
Heat: Card shouldn't generate much heat, airflow might not be great
Noise: Headphones will fix that
HP link:http://support.hp.com/us-en/product/HP-Pavilion-p7-Desktop-PC-series/5187022/model/5193525/product-info