This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.
There were 58 solutions found in 1642.07 seconds (with a Bezout bound of 36000).
Reference: "Methods and applications of interval analysis" by Ramon E. Moore (p. 64).
See also: http://homepages.math.uic.edu/~jan/Demo/rabmo.html.
i1 : rabmo(QQ)
2 2
o1 = {x + x + x + 2x - 1, x x + x x + 2x x + 2x x + 2x x - -, x x +
1 3 5 7 1 2 3 4 5 6 7 8 7 9 3 1 2
------------------------------------------------------------------------
2 2 2 2 2 3 3 3 3 3
x x + 2x x + 2x x + 2x x - -, x x + x x + 2x x + 2x x + 2x x -
3 4 5 6 7 8 7 9 5 1 2 3 4 5 6 7 8 7 9
------------------------------------------------------------------------
2 4 4 4 4 4 2 2 1 4
-, x x + x x + 2x x + 2x x + 2x x - -, x x + 2x x x - -, x x +
7 1 2 3 4 5 6 7 8 7 9 9 5 6 7 8 9 9 5 6
------------------------------------------------------------------------
2 2 1 3 2 2 1 4 3 3 1
2x x x - --, x x + x x x + x x x - --, x x + x x x + x x x - --}
7 8 9 25 5 6 7 8 9 7 8 9 15 5 6 7 8 9 7 8 9 21
o1 : List
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The object rabmo is a method function.