jmc

Based on the expansion $(x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta ,$ we know that the product of a quadratic formula with leading term of $x^2$ is just the constant term.

In this case, we rearrange the equation given to look like the derived equation above--i.e. $x^2+2x-35=0.$ Now, we see that the product of the roots is just $\boxed{-35}.$