Question

select the approximate values of x that are solutions to f(x) = 0, where f(x) = -8^2 + 2x + 2

Answer 1

How approximate?
Assuming you meant f(x) = -8x^2 + 2x + 2,
f(-1) = -10
f(0) = 2
f(1) = -6

So, f(x)=0 somewhere in (-1,0) and (0,1).

You can, of course, use the quadratic formula to get an exact answer and then approximate with as many decimal places as you wish. See

http://www.wolframalpha.com/input/?i=-8x^2+%2B+2x+%2B+2