WE PROPOSE AN IN-DEPTH X-RAY STUDY OF FAST-EVOLVING BLUE OPTICAL TRANSIENTS (FBOTS). FBOTS ARE A NEW CLASS OF COSMIC EXPLOSIONS WITH LUMINOSITIES AND TIME SCALES OF EVOLUTION THAT CHALLENGE TRADITIONAL SUPERNOVA (SN) MODELS. ALTERNATIVE SCENARIOS INCLUDE A FAILED SN OF A STRIPPED STAR THE DETONATION OF A HELIUM SHELL ON A WHITE DWARF AND A SN SHOCK BREAKING OUT FROM A DENSE CIRCUMSTELLAR MEDIUM. TO DATE RAPIDLY EVOLVING LUMINOUS TRANSIENTS HAVE MOSTLY BEEN STUDIED IN THE OPTICAL/UV REGIME WHICH IS OF THERMAL ORIGIN AND IT IS NOT SENSITIVE TO THE NATURE OF THE UNDERLYING ENERGY SOURCE AND THE PROPERTIES OF THE EXPLOSION'S FASTEST EJECTA. HERE WE PROPOSE TO CAPITALIZE ON OUR RECENT DISCOVERY OF THE FIRST X-RAY EMISSION FROM A FBOT AND START THE FIRST X-RAY MONITORING CAMPAIGN OF NEARBY FBOTS. THE PRIMARY GOALS ARE TO (I) OBTAIN THE FIRST CONSTRAINTS ON THE MASS-LOSS HISTORY OF THE STELLAR PROGENITORS OF A NEW CLASS OF SN EXPLOSIONS; (II) TEST THE PRESENCE OF ENGINES DRIVING THE EXPLOSIONS.