How do you calculate the proportion of alleles using the Hardy -Weinberg equation with 2 loci?

by Shuffler
(UK)

There are 4 genotypes with the following qtys, some alleles are known, some are not:

1,A? B? 61

2,aa bb 17

3,aa B? 4

4 A? bb 1

aa bb = q^2 = 17/83 = 0.205 = Homozygous recessive genotype
q = 0.453 = Recessive allele frequency
p = 1- 0.453 = 0.547 = Dominant allele frequency

plug into P^2 + 2pq + q^2 = 1

0.205 + 0.499 + 0.299 = 1.

I'm not confident this is correct, I've seen another method which is much more complex with a different answer. I don't understand the logic used with the complex method,hence I can't use it.