The version with about 0.13 is not an especially good fit; it has a sum-of-squared-errors of about 0.06 for the fsolve.
You can do better near 0.08. In particular, the following x has a SSE of about 1E-16 for the fsolve:
2.41822013449192763, 0.393312505963807846, 0.463898429336224605, 1.00253486482090381, 0.345768760645462359, 0.290239202125991747, 1.37204767772094183, 0.0843373491237134065, 0.927918117994239955