Originally Posted by cherokeesam
At a New Years' Eve party 13 years ago! While he was drunk! And getting laid! With a box of scraps!
Tony didn't completely solve the problems with Extremis back then, though he made a good start at figuring it out. Maya and Killian wanted him to complete the work for him, hence their using Extremis on Pepper to give him an incentive. In Killian's case, torturing Pepper for rejecting him was just a side bonus.
After then final battle Tony told Pepper that he could "fix" her because he had almost solved the problems years before. Once the dust settled he finished working out the algorithm and used the corrected formula on Pepper. This was similar to the comic book, where Tony created his own version of Extremis that gave him different abilities while saving his life. It seemed to me that the fix should have left Pepper with her Extremis enhancements but no longer prone to spontaneous combustion but I don 't think that's what Pearce & Black were going for.
Kevin Feige said that Extremis will be used again in the MCU, so we may well see other characters with enhanced powers from the formula. Even though Killian is (presumed) dead, AIM and its mad scientists must still be creeping around out there which makes them an ongoing threat. Perhaps some of Killian's Extremis soldiers survived or weren't in that last battle, so they live to fight another day. AIM might also be creating new Extremis-powered threats for its own purposes. It will be interesting to see whether that thread is picked up in other films or the SHIELD TV show.