GMAT Math

Q) If x = -5 + ( 45 +4k - k2 )0.5 where k is a positive integer. How many values of k exists if x has to be positive?

x = -5 + ( 45 +4k - k^2 )0.5 >0
35 + 4k - k^2 >0
or k^2 - 4k - 35 <0
Do you have options??

using the quadratic equation, for the expression k^2 - 4K - 35 to equal zero, k would have to equal 2+ Sqrt(39). That would give you a value either slightly less than -4 or slightly more than +8. The values that make x positive will be in that range. Ignoring the negative integers and zero, you get 1,2,3,4,5,6,7, and 8. Answer 8.