We study the dark energy equation of state as a function of redshift in a nonparametric way, without imposing any a priori w (z) (ratio of pressure over energy density) functional form. As a check of the method, we test our scheme through the use of synthetic data sets produced from different input cosmological models that have the same relative errors and redshift distribution as the real data. Using the luminosity-time correlation for gamma-ray burst (GRB) X-ray afterglows (the Dainotti et al. correlation), we are able to utilize GRB samples from the Swift satellite as probes of the expansion history of the universe out to z 10. Within the assumption of a flat Friedmann-Lemaître-Robertson-Walker universe and combining supernovae type Ia (SNeIa) data with baryonic acoustic oscillation constraints, the resulting maximum likelihood solutions are close to a constant w = –1. If one imposes the restriction of a constant w , we obtain w = -0.99 0.06 (consistent with a cosmological constant) with the present-day Hubble constant as and density parameter as , while nonparametric w (z) solutions give us a probability map that is centered at and . Our chosen GRB data sample with a full correlation matrix allows us to estimate the amount, as well as quality (errors), of data needed to constrain w (z) in the redshift range extending an order of magnitude beyond the farthest SNeIa measured.