My suggestion would be classify the solutions based on how many zeros in x[i]. The more zeros, the easier to find with FindRoot
. Based on the generic pattern of your equations,
a*x^2+x == 0
I feel most x's would be quite small. The solution with least zeros so far I have found is this one:
{Subscript[x, 1]->0.049298,Subscript[x, 3]->0.115546,Subscript[x, 4]->-0.0294936,Subscript[x, 5]->-0.080845,Subscript[x, 6]->0.0596149,Subscript[x, 7]->0.0875315,Subscript[x, 8]->0.000925203,Subscript[x, 10]->0.00173587,Subscript[x, 11]->-0.0186874,Subscript[x, 12]->-0.0164931,Subscript[x, 13]->0,Subscript[x, 14]->0.049294,Subscript[x, 15]->0.0465952,Subscript[x, 16]->0.00177485,Subscript[x, 17]->0.00182401,Subscript[x, 21]->0.00114009,Subscript[x, 22]->0.00127775,Subscript[x, 23]->0.00149794,Subscript[x, 24]->0,Subscript[x, 26]->0,Subscript[x, 27]->0.138165,Subscript[x, 28]->0.080892,Subscript[x, 29]->0.080892,Subscript[x, 30]->0}