Answer:
 AB = 28
Step-by-step explanation:
A midsegment joins midpoints of sides of the figure. In this problem, the midsegment is irrelevant.
What is important is that D is the midpoint of AB. That means ...
 AD = DB
 x^2 -x +2 = x^2 -2x +6
 x = 4 . . . . . . . add 2x -2 -x^2 to both sides
The length of AD is then ...
 AD = x^2 -x +2 = 4^2 -4 +2 = 16 -4 +2 = 14
AD is half the length of AB, so ...
 AB = 28
