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 D.  9
Step-by-step explanation:
The segment lengths are equal, so ...
 x^2 = 90-x
 x^2 +x -90 = 0 . . . . . . add x-90 to put in standard form
 (x +10)(x -9) = 0 . . . . . factor
The solutions are the values of x that make the factors zero: -10, 9.
The positive value of x is 9.