Algebra: A Combined Approach (4th Edition)

$-1, -8$
Let $a$ and $b$ be the two numbers. $ab=8$ $a+b=-9$ $a=-9-b$ $(-9-b)b=8$ $-9b-b^2=8$ $b^2+9b+8=0$ $(b+8)(b+1)=0$ $b=-1$ or $-8$ If $b=-1$, then $a=-8$. If $b=-8$, then $a=-1$. Therefore, the two numbers are $-1$ and $-8$.