Approximate the zeros of the function. round to the nearest tenth if necessary. f(x) = 4x^2 + 4x - 35. explain each step on how you got there.

4x²+4x-35=0
factor: (2x+7)(2x-5)=0
2x+7=0, or 2x-5=0
2x=-7 or 2x=5
x=-3.5 or x=2.5

I don't see any rounding necessary in this case. 

when you factor ax²+bx+c, you take the two factors of a and the two factors of c, one factor of a times one factor of c, the other factor of a times the other factors, the sum of the two products make b.
in this case, the factors of 4 is 2 and 2, the factors of -35 is -5 and 7. I line them up in the following way:
2    -5

2      7
then I multiple them diagonally, the top left 2 multiplying the bottom right 7=14, and the other 2 multiplying -5=-10, 14 and -10 make a sum of 4.

if you don't get the desired sum, switch the factors up and down till you have the right combination. Note: Do not switch left and right. 

I hope this makes sense to you.