[Coda]

So the part that's confusing you -- and a small mistake Serra made -- is that the formula is specifically x = v_meant. It's not supposed to be the initial speed for the whole distance, it's the average speed.

For uniform acceleration, you should remember this from last semester:
v_mean = (v₀ + v_f)/2.

So Serra's math is off by a factor of 2, because the average speed during braking is not 88 ft/sec, but 44 ft/sec.

The rest of the process is correct:

x = v_meant
146 ft = (44 ft/sec) * t
t = (146 ft) / (44 ft/sec) ~= 3.32 sec

a = Δv/t
a = (-88 ft/sec) / (3.32 sec) -- this one is still 88 because it's the total change in velocity, not the average
a = -26.5 ft/sec²

EDIT: If you want to use v_f² = v_i² + 2a(x_f-x_i) you can, and it gives you the same result:

0 = (88 ft/sec)² + 2a(146 ft)
-7744 ft²/sec² = 2a(146 ft)
-53.0 ft/sec² = 2a
-26.5 ft/sec² = a

EDIT 2: Also your initial answer of 6.50x10⁴ mi/h² was in fact correct:

(65000 mi/h²) / (3600 sec/h) / (3600 sec/h) * (5280 ft/mi) = 26.48 ft/sec²

Dimensional analysis is a wonderful thing. :P