The problem set text suggests solving the equation
by recursively solving the equation
but what is the relation between both?
The relation is given by the equation
which if we substitute into equation 1 will give us
Gathering all the terms involving b together, and all those
involving r together,
we can re-write Equation 4
to look like
Comparing Equations 5 and 2, we can see that we can equate
But the problem suggests we first solve Equation 2
and use its solutions
to solve 1, so we need to re-write Equation 6
to yield
That's all we need. Recursively solving Equation 2
will give us values for 
and 
,
which we will plug into Equation 7 (with our current
value for the quotient q)
to produce the solution to the main equation 1.
