High-pressure x-ray diffraction of (Mg0.80 Fe0.20)O at room temperature reveals a discontinuity in the bulk modulus at 40 (±5) GPa, similar to the pressure at which an electronic spin-pairing transition of Fe2+ is observed by Mössbauer spectroscopy. We determine the zero-pressure bulk modulus of low-spin magnesiowüstite to be between K70=136 and 246 GPa, with a pressure derivative (∂Kτ/∂P)τ0 between 5.2 and 3.9. The best fit unit-cell volume at zero pressure, V0=71 (±5) Å, is consistent with past estimates of the ionic radius of octahedrally-coordinated low-spin Fe2+ in oxides. A spin transition at lower-mantle depths between 1100 and 1900 km (40-80 GPa) would cause a unit-cell volume decrease (ΔV) of 3.7 (±0.5) to 2.0 (±0.1) percent and bulk sound velocity increase (Δvø) of 7.6 (±4) percent at 40 GPa and 7.6 (±1.2) percent at 80 GPa. Even in the absence of a visible seismic discontinuity, we expect the spin transition of iron to imply correction to current compositional models of the lower mantle, with up to 10 mol percent increase of magnesiowüstite being required to match the seismological data.