Answer:
none
Step-by-step explanation:
The domain of the equation can be found by looking at the requirements ...
- the square root is non-negative
- the argument of the square root is non-negative.
Domain
For n+2 ≥ 0, we find ...
n ≥ -2 . . . . . . . . subtract 2 from both sides
For -16-5n ≥ 0, we find ...
-16 ≥ 5n . . . . . add 5n
-3.2 ≥ n . . . . . divide by 5
Together, these domain restrictions require that ...
n ≥ -2
n ≤ -3.2
These intervals do not overlap, so there are no values of n that can satisfy this equation.
__
Additional comment
The solutions would appear on the attached graph as points where the curves intersect above the x-axis. They do not intersect, hence the equation has zero solutions.
__
If we were to solve this without regard to domain restrictions, we would square both sides to get ...
(n +2)² = -16 -5n
n² +9n +20 = 0 . . . . . put in standard form
(n +4)(n +5) = 0 . . . . . factor
n = {-5, -4} . . . . . . . . . both are extraneous solutions.
These "solutions" do not satisfy the requirement that the square root be positive.
