Related Rates: Check my work

At a price of $p the demand x per month (in multiples of 100) for a piece of software is:

x^2 +2xp +2p^2 =500

The manufacturer is increasing the price at a rate of 20 cents per month. Find the corresponding rate of decrease in demand for the software when the software costs $10.

dp/dt= 20 cents/month

p=10

dx/dt=?

x=?

Because x was not given I plugged in dp/dt and p into the original equation, plugged it into the quadratic formula and came up with x= 10.

Then I took the derivative of the original eq:

2x(dx/dt)+2(x(dp/dt)+p(dx/dt))+4p(dp/dt)=0

And I plugged everything else in and came up with dx/dt=30

Did I solve this correctly? Should I have put .20(dollars/month) instead of 20 (cents/month)?

Thanks!