You entered:
x1+x2+x3+x4+x5+x6+x7+x8=0
What you mean?
x1+x2+x3+x4+x5+x6+x7+x8=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
x81 = -x1 - x2 - x3 - x4 - x5 - x6 - x7
$$x_{81} = - x_{1} - x_{2} - x_{3} - x_{4} - x_{5} - x_{6} - x_{7}$$
Sum and product of roots
[src]
0 + -x1 - x2 - x3 - x4 - x5 - x6 - x7
$$\left(- x_{1} - x_{2} - x_{3} - x_{4} - x_{5} - x_{6} - x_{7}\right) + 0$$
-x1 - x2 - x3 - x4 - x5 - x6 - x7
$$- x_{1} - x_{2} - x_{3} - x_{4} - x_{5} - x_{6} - x_{7}$$
1*(-x1 - x2 - x3 - x4 - x5 - x6 - x7)
$$1 \left(- x_{1} - x_{2} - x_{3} - x_{4} - x_{5} - x_{6} - x_{7}\right)$$
-x1 - x2 - x3 - x4 - x5 - x6 - x7
$$- x_{1} - x_{2} - x_{3} - x_{4} - x_{5} - x_{6} - x_{7}$$
-x1 - x2 - x3 - x4 - x5 - x6 - x7