If Statement Inside Nested For Loop

The If statement inside my nested for loop is not executing. Instead, the code essentially ignores it and prints all possible combinations of x_1, x_2, x_3, x_4, x_5, x_6, and x_7 instead of the ones specified by the if statement.

I've tried avoiding using a nested for loop altogether using zip, but this only looks at combinations of x_1, x_2, x_3, x_4, x_5, x_6 and x_7 where x_1 == x_2 == x_3 == x_4 == x_5 == x_6 == x_7. I've also tried placing the if statement in various places, but each time, the code ignores the statement.

for a in range(-5,6):
    for b in range(-5,6):
        for c in range(-5,6):
            for d in range(-5,6):
                for e in range(-5,6):
                    for f in range(-5,6):
                        for g in range(-5,6): 
                            for x_1 in range(-5,6): 
                                for x_2 in range(-5,6): 
                                    for x_3 in range(-5,6): 
                                        for x_4 in range(-5,6): 
                                            for x_5 in range(-5,6): 
                                                for x_6 in range(-5,6): 
                                                    for x_7 in range(-5,6):
                                                        if a*x_1 + b*x_2 + c*x_3 + d*x_4 + e*x_5 + f*x_6 + g*x_7 == 7 and x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 + x_6^2 + x_7^2 == 7:
                                                            print x_1, x_2, x_3, x_4, x_5, x_6, x_7                                                                                                                        
print "DONE"

It shouldn't output every single combination of x_1, x_2, x_3, x_4, x_5, x_6 and x_7 as it does not. It should only output, for example, 1, 1, 1, 1, 1, 1, 1 -- this is a combination of x_1, x_2, x_3, x_4, x_5, x_6, and x_7 such that the sum of all the squares of the seven variables is equal to 7 and ax_1 + bx_2 + cx_3 + dx_4 + ex_5 + fx_6 + g*x_7 is equal to 7 for some a,b,c,d,e,f, and g each any number in range(-5,6) (in particular, in this example, each of these 7 letter variables is just equal to 1). All 7 of x_1, x_2, ..., x_7 need not be equal, either.