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High-Tc cuprate superconductors display startling nanoscale inhomogeneity in essential properties such as pseudogap energy scale, Fermi surface, and even superconducting critical temperature. The direct cause of this inhomogeneity has remained mysterious; theoretical explanations have ranged from chemical disorder to spontaneous electronic phase separation.  We extend the energy range of scanning tunneling spectroscopy, allowing the first complete mapping of all three types of oxygen dopants in Bi_2+ySr_2-yCaCu₂O_8+x with maximum superconducting T_c ~ 90K. We show that a subset of these dopants are indeed the hidden variable at the root of the nanoscale disorder. We explain how the spatial variations in competing electronic orders, such as the pseudogap and the charge density wave, are governed by the disorder in the dopant concentrations, which suggests a possible avenue to raise T_c in this material.