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 double the energy range of scanning tunneling spectroscopy, allowing the first complete mapping of all three types of oxygen dopants in Bi2+ySr2-yCaCu2O8+x with maximum superconducting Tc ~ 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 coexisting electronic orders, such as the pseudogap and the charge density wave, are governed by the disorder in the dopant concentrations, particularly vacancies in the apical oxygen site. Our findings suggest a possible avenue to raise Tc in this material.