Question

What two numbers add up to 1 but multiply to -30

Answer 1

$x;\ y-the\ numbers\\\\ \left\{\begin{array}{ccc}x+y=1&\to x=1-y\\xy=-30\end{array}\right\\\\subtitute\ x=1-y\ to\ second\ equation:\\\\(1-y)y=-30\\y-y^2+30=0\\-y^2+y+30=0\ \ \ \ \ |change\ signs\\y^2-y-30=0\\y^2-6y+5y-30=0\\y(y-6)+5(y-6)=0\\(y-6)(y+5)=0\iff y-6=0\ or\ y+5=0\\\Downarrow\\y=6\ or\ y=-5$

$x=1-y\\\\for\ y=6\Rightarrow x=1-6=-5\\\\for\ y=-5\Rightarrow x=1-(-5)=1+5=6\\\\=======================================\\Answer:\boxed{6}\ and\ \boxed{-5}$