what two numbers multiply to 394.24 and adds up to 40?

what two numbers multiply to 394.24 and adds up to 40 ?

$$\small{\text{
\boxed{
\begin{array}{rcl}
x_1+x_2 &=& 40 \\ \quad x_1*x_2 &=& 394.24
\end{array}
}
}}$$

$$\small{\text{
set $x^2 - (x_1+x_2)x + x_1*x_2 = 0$
}}
$\\$ \small{\text{
than we have $x^2 - 40x + 394.24 = 0$
}}
$\\$ \small{\text{
and the solution for $x_1$ and $x_2$ is: $\frac{ -b\pm\sqrt{b^2-4ac} } {2a}$
}}
$\\$ \small{\text{
$x_{1,2}=\frac{ 40\pm\sqrt{1600-4*394.24 } } {2}
= \frac{ 40\pm\sqrt{23.04} }{2}
= \frac{ 40\pm4.8 }{2}
$
}}
$\\$ \small{\text{
$x_1=\frac{ 40+4.8 }{2} = 22.4
$
}}
}}
$\\$ \small{\text{
$x_2=\frac{ 40-4.8 }{2} = 17.6$
}}$$

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 !!!