I am looking for a numerical method that can solve a system of non-linear equations. The non-linear equations are polynomials that are in one of the following forms:
$$ c_1x_1+c_2x_2+\ldots+c_nx_n=C \\ d_1x_1^2+d_2x_2^2+\ldots+d_nx_n^2=D $$
(The variables are $x_1,x_2,\ldots x_n$.)
I can't get initial guesses that are close to the root. Is there a good numerical method to solve the system of equations?
Thank you in advance