© 2016 The Authors. With the largest spectroscopic galaxy survey volume drawn from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), we can extract cosmological constraints from the measurements of redshift and geometric distortions at quasi-linear scales (e.g. above 50 h-1 Mpc). We analyse the broad-range shape of the monopole and quadrupole correlation functions of the BOSS Data Release 12 (DR12) CMASS galaxy sample, at the effective redshift z = 0.59, to obtain constraints on the Hubble expansion rate H(z), the angular- diameter distance DA(z), the normalized growth rate f(z)σ8(z), and the physical matter density Ωm h2.We obtain robust measurements by including a polynomial as the model for the systematic errors, and find it works very well against the systematic effects, e.g. ones induced by stars and seeing. We provide accurate measurements (DA(0.59)rs,fid/rs, H(0.59)rs/rs,fid, f(0.59)σ8(0.59), Ωm h2) = (1427 ± 26 Mpc, 97.3 ± 3.3 kms-1 Mpc-1, 0.488 ± 0.060, 0.135 ± 0.016), where rs is the comoving sound horizon at the drag epoch and rs,fid = 147.66 Mpc is the sound scale of the fiducial cosmology used in this study. The parameters which are not well constrained by our galaxy clustering analysis are marginalized over with wide flat priors. Since no priors from other data sets, e.g. cosmic microwave background (CMB), are adopted and no dark energy models are assumed, our results from BOSS CMASS galaxy clustering alone may be combined with other data sets, i.e. CMB, SNe, lensing or other galaxy clustering data to constrain the parameters of a given cosmological model. The uncertainty on the dark energy equation of state parameter, w, from CMB+CMASS is about 8 per cent. The uncertainty on the curvature fraction, Ωk, is 0.3 per cent. We do not find deviation from flat ΛCDM.