This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-4258U CPU at 2.40GHz.
There were 16 solutions found in 0.707914 seconds (with a Bezout bound of 96).
Reference: A.P. Morgan. Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems', Prentice-Hall, Englewood Cliffs, N.J., 1987. Chapter 9.
See also: http://homepages.math.uic.edu/~jan/Demo/comb3000s.html
i1 : comb3000s(RR_53)
o1 = {.101815x + .98961x + 1.34637x + 3.4697x - 2.12454, .57674x +
2 6 9 10 3
------------------------------------------------------------------------
.78995x - 2.19493, .087316x + .895129x + 1.37722x + 2.45208x +
8 1 3 5 8
------------------------------------------------------------------------
.719622x + .927261x - 5.67773, .0025003x + 19.9988x - 19.9988, -
9 10 4 7
------------------------------------------------------------------------
2 2 2
1.37722x + .726099x , - .98961x + 1.0105x , - 19.9988x + .050003x , -
1 5 2 6 4 7
------------------------------------------------------------------------
2
1.93702x x + .516256x , - .968878x x + 1.03212x , - 3.21732x x +
1 3 8 1 2 9 1 2
------------------------------------------------------------------------
.310818x }
10
o1 : List
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The object comb3000s is a method function.