Great information, everyone. Thank you.
A followup question. I am thinking about purchasing a house later this year. If I were to open up two new cards, roughly how long would it take for my score to recover from this? Are we talking a couple months or a couple years?
Buying a house changes everything. What are your scores now? If high enough you might want to wait until AFTER you buy to apply for any new credit. If your scores aren't high enough and you want the new credit to raise your scores then generally you should apply at least 6 months before trying to qualify to buy.
And maybe only apply for 1 new card until after you buy.