We present a precision measurement of the top-quark mass using the full sample of Tevatron √s = 1.96 TeV proton-antiproton collisions collected by the CDF II detector, corresponding to an integrated luminosity of 8.7 fb(-1). Using a sample of tt¯ candidate events decaying into the lepton+jets channel, we obtain distributions of the top-quark masses and the invariant mass of two jets from the W boson decays from data. We then compare these distributions to templates derived from signal and background samples to extract the top-quark mass and the energy scale of the calorimeter jets with in situ calibration. The likelihood fit of the templates from signal and background events to the data yields the single most-precise measurement of the top-quark mass, M(top)=172.85±0.71(stat)±0.85(syst) GeV/c(2).