Question 337287
This may not be the exact answer or correct reason, you can compare the results with other answers.

Solving your quadratic equation using standard formula gives imaginary roots for x.
i.e. x = (0.6 + i2.6) or x = (0.6 - i2.6)

Considering the second requirement, i.e the cost C(x) to be minimum, take first derivative of the equation and evaluate to zero. This gives,

dC(x)/dx = 0.5*2*x - 0.6 = 0
x = 0.6
This means 0.6 * 100 = 60 bicycles.

Verify the result:
For x = 60, C(x) = 1768 dollars. Avg = $29.45
For x = 70, C(x) = 2411 dollars. Avg = $34

For x = 50 or less, the Avg values are lesser than $29.45. I hope this helps.