Observe that the first key polynomial from the
above spreadsheet is quadratic in b.
We could complete the square and put the polynomial
in the form
(6.10)(b + ) (b + ) +
where and are expressions involving , , , , A, , , and . Since there are many unknowns in the problem, there is probably excess freedom. Let us investigate what happens when we take . This yields the polynomial equation
which we could add to the starting polynomial equations and proceed. We can also complete the square for the expression in c and put that expression in the form
We also assume that . This defines c by the following equation
Since we have now solved for b and c, we can use these equations to solve for and .