Excel found a solution to this but it's not pretty: (Be sure to remove the constraint on nonnegative integers)
x1=-.578
x2=-2.15
x3=4.85
x4=-1.27
x5=-1.22
x6=2.03
To set up Solver you want to set x1 through x6 as inputs, set the sum of each combination as one half of the constraints and the numbers (-4,9,0) as the other half. Then choose one sum as the target cell to equal its equivalent right half (-4,9,0). I chose -4. Set your constraints to have your respective sums equal its right halves. Unclick the constraint for nonnegative integers and Solve! Be prepared for some ugly negative integers. Please attach a picture of your Solver setup if you have questions.
Hope that helps,
Deanna
