Set the actual function itself equal to 0 to find the appropriate x-values.

-2^2 + 7x + 2 = 0

4 + 7x + 2 = 0

7x + 6 = 0

7x = -6

x = -6/7

f(-6/7) = 4 + 7(-6/7) + 2 = 4 + 2 - 6 = 6 - 6 = 0

(-6/7, 0)

So, plugging in -6/7 for x will give you f(-6/7)=0, therefore making -6/7 an appropriate x-value for this question.