Do you think this will fit inside the Alienware x51 and work with my motherboard?
that card will not fit. it's over 10 inches long, and the max space you have for a graphics card in the X51 is 9.5 inches. I recommend this card for your upgrade:
Also, make sure you have the 330W power brick. get the Model number off of your brick and google it. my model number is DA330PM111, which is the 330W brick.