what equals 7 when multiplied but -6 when added?

Let  xy = 7    and x + y = -6    

Using the second equation  we have y = -6 - x

So....substituting this into the first equation, we have

x (-6 - x)  = 7 simplify

-6x - x^2  = 7      rearrange

x^2 + 6x + 7 = 0   using the onsite calculator we have

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{2}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{2}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{4.414\: \!213\: \!562\: \!373\: \!095}}\\
{\mathtt{x}} = -{\mathtt{1.585\: \!786\: \!437\: \!626\: \!905}}\\
\end{array} \right\}$$

So these are the two interchangeable answers for x and y.......

And as Annabelle1DirectionS found, there are no integer solutions......!!!!

The only whole number I can think of when multiplying is 7 and 1. But when adding even when you change both to negatives the answer will be too big. When you change one to a negative and leave one positive, the answer wouldn't equal 7 when you multiply them together.