  We present first results from a first-principles calculation of the QCD
equation of state to $\mathcal{O}(\mu_B^4)$, where $\mu_B$ is the baryon
chemical potential. We find that second-order corrections are sufficient for a
large part of the freeze-out temperature and baryon chemical potential range
achieved by the RHIC beam energy scan. Nevertheless, higher-order corrections
are necessary to extend the validity of the equation of state down to beam
energies $s^{1/2}_{NN}\sim 20$ GeV.
