The two-dimensional model which emerges from low-energy considerations of string theory is written down. Solutions of this classical model are noted, including some examples which have nontrivial tachyon field. One such represents the classical backreaction of the tachyon field on the black hole for a two parameter set of tachyon potentials. Assuming the classical black hole background in the `Eddington-Finkelstein' gauge, the tachyon equation is separable and the radial part is solved by a hypergeometric function, which is in general of complex argument. A semi-classical prescription for including the quantum effects of the tachyon field is described, and the resulting equations of motion are found. Special solutions of these equations are written down.

13 pages, published version, now in Latex, minor revisions, references amended