Let
f(n) = n^2 - 2 if n < 0
f(n) = 2n - 28 if n >= 0
What is the positive difference between the two values of a that satisfy the equation f(-2) + f(2) + f(a) = 0?
+152 first, we should calculate the values of f(-2) and f(2) to be able to simplify the equation.
-2 is less than 0, so we're using the first function.
f(-2) = (-2)^2 - 2 = 4 - 2 = 2.
2 is greater than 0, so we're using the second function.
f(2) = 2(2) - 28 = 4 - 28 = -24
now let's plug it back into the equation and solve for a.
2 - 24 + f(a) = 0.
-22 + f(a) = 0
f(a) = 22.
since we now know what f(a) can be, we can work backwards using the two given functions.
let's start with the first function.
n^2 - 2 = 22
n^2 = 24
n = -sqrt(24) , as it's the only value less than 0 that satisfies the equation. (THOUGH: i'm not completely sure about this...)
second function,
2n - 28 = 22
2n = 50
n = 25
so we get our difference to be 25 - (-sqrt(24)) which is 25 + sqrt24, or 25 + 2sqrt6.
i'm not completely sure about this answer though, hopefully it still helped you get some general idea of the problem - please let me know if you have any follow-up questions! 
