So
x + y = 40 → y = 40 - x
And
xy = 394.24
And substituting for y in the second equation, we have
x(40 - x) = 394.24 simplify
40x - x^2 = 394.24 multiply everything by 100
4000x - 100x^2 = 39424 rearrange
100x^2 - 4000x + 39424 = 0 this might be a little difficult to factor directly.... using the onsite solver, we have
$${\mathtt{100}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4\,000}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{39\,424}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{112}}}{{\mathtt{5}}}}\\
{\mathtt{x}} = {\frac{{\mathtt{88}}}{{\mathtt{5}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{22.4}}\\
{\mathtt{x}} = {\mathtt{17.6}}\\
\end{array} \right\}$$
And there are the two numbers... if x = 22.4, then y = 17.6 .......or vice-versa........I didn't anticipate that we might get a "clean" answer like that !!!
