Iron in the major lower mantle (LM) minerals undergoes a high spin (HS) to low spin (LS) transition at relevant pressures (23-135 GPa). Previous failures of standard first principles approaches to describe this phenomenon have hindered its investigation and the clarification of important consequences. Using a rotationally invariant formulation of LDA+U we report a successful study of this transition in low solute concentration magnesiowüstite, (Mg1-xFex)O, (x<0.2), the second most abundant LM phase. We show that the HS-LS transition goes through an insulating (semiconducting) intermediate mixed spins (MS) state without discontinuous changes in properties, as seen experimentally. We show that the HS state crosses over smoothly to the LS state passing through an insulating MS state where properties change continuously, as seen experimentally.