You are not going to be able to find a closed form algebraic solution for this.
If you take the first 6 equations and solve them for the first 6 variables, then you will find that some of the values become framed in terms of the roots of a quintic polynomial; the roots of such polynomials are not expressible in closed form solutions.
If you take the first 6 equations and solve for x(1) to x(5) and x(8) (rather than x(6)) then you will get repeated subexpressions involving the square root of an expression in x6. This immediately puts a constraint on x6, that the subexpression must be non-negative (unless you are hoping that imaginary-valued expressions will exactly cancel out to give real values) The interior expression is of the form
x6^2 * (x6 + c) * f(x6)
where c is a numeric constant and f(x6) is a quartic. Solving for the boundary condition that this expression becomes 0, x6 must be 0, or x6 must be -c, or the quartic must be 0. Fortunately there are exact solutions to quartics. The bad news is that the coefficients for the quartic are all on the order of 10^37, so you will not be able to find correct-enough numeric solutions with double precision numbers as those are only precise for integers up to about 10^16 . Therefore you will need to switch to the Symbolic Toolbox and push up the number of working digits.
The excluded zone for x6 (where the interior expression goes negative) is from approximately -33 to -20. For one of the solution paths, at least.
Can you place additional constraints on the variables beyond that they must be real-valued? For example if you were to tell me that x6 is going to be -25 +/- 5 then I could eliminate a large solution branch.
