I've tried using matrices, and it has failed. I've looked at external modules and external programs, but none of it has worked. If someone could share some tips or code that would be helpful, thanks.
import numpy
import scipy.linalg
m = numpy.matrix([
[1, 1, 1, 1, 1],
[16, 8, 4, 2, 1],
[81, 27, 9, 3, 1],
[256, 64, 16, 4, 1],
[625, 125, 25, 5, 1]
])
res = numpy.matrix([[1],[2],[3],[4],[8]])
print scipy.linalg.solve(m, res)
returns
[[ 0.125]
[-1.25 ]
[ 4.375]
[-5.25 ]
[ 3. ]]
(your solution coefficients for a,b,c,d,e)