Question

What multiplys to be ten and adds to be negative 3

Answer 1

$x;\ y-the\ numbers\\\\ \left\{\begin{array}{ccc}xy=10&(1)\\x+y=-3&(2)&x=-3-y\end{array}\right\\\\subtitute\ x=-3-y\ to\ (1)\\\\(-3-y)y=10\\-3y-y^2=10\\y^2+3y-10=0\\y^2+5y-2y-10=0\\y(y+5)-2(y+5)=0\\(y+5)(y-2)=0\iff y+5=0\ or\ y-2=0\\y=-5\ or\ y=2\\\\subtitute\ to\ (2)\\x=-3-(-5)=-3+5=2\ or\ x=-3-2=-5\\\\Answer:2\ and\ -5.$