The determination of the three-dimensional structure of a weak protein-protein complex in solution using small-angle X-ray scattering requires the deconvolution of its contribution from those of other components coexisting in equilibrium. Using the oligomerization equilibrium of low molecular weight phosphatase (ImwPTP) as a model system, we show computationally and experimentally that the individual low-resolution structures of monomeric and dimeric lmwPTP can be determined from a small number of SAXS curves using the multivariate curve resolution with alternating least squares (MCR-ALS) algorithm. The dimeric complex represents no more than 15% of the macromolecules in the most concentrated sample. The derived structures are in good agreement with the crystallographic ones and the dissociation constant matches the one measured by NMR. These results demonstrate the power of SAXS, in combination with MCR-ALS, to study transient biomolecular complexes. The limits of the method were explored using a three-species model that describes the oligomerization of lmwPTP at higher concentrations.