Observation of neutrinoless double-beta decay (0νββ) would constitute discovery of a new class of particle (the Majorana neutrino), violate lepton number conservation, and provide a constraint on the neutrino mass scale. The Enriched Xenon Observatory experiment (EXO-200) operated an extremely radio-pure tracking calorimeter filled with liquid xenon enriched in the candidate isotope 136Xe and installed underground in New Mexico, USA. The author presents a search for 0νββ with the complete EXO-200 dataset, the second-largest exposure of any 0νββ experiment (234.1 kg∙yr). The analysis applied coupled fits to event energy and position with a classical topological discriminator. The author produced an expanded background model to search for radioactive 42Ar via its β-decay product, 42K. No signal excess was observed near the 0νββ Q-value, leading to a limit on the 0νββ half-life in 136Xe of T_(1/2)^0ν >3.0×10^25 yr and Majorana neutrino mass 〈m_ββ 〉<(100-309) meV, both reported at the 90% confidence level (CL). The corresponding sensitivity of 4.2×10^25 yr (90% CL) represents an improvement of 5.7% over the standard EXO-200 background model, which does not include 42Ar. Notably, the author's expanded model has been used to publish the first constraint on the content of 42Ar in enriched xenon, which provides important input to the design of future low-background experiments. A limit is set on the specific activity of 42Ar in enriched xenon at <0.8 μBq/kg (90% CL). Additionally, the author’s improvements to offline event reconstruction techniques, operational responsibility for the EXO-200 scintillation panel detectors, and principal contributions to a published paper on cosmogenic backgrounds are also discussed.