The quadratic equation $x^2-5x+5=-4x+7$ has two roots. Find the absolute difference of these roots.
1 answer
To solve the given equation, we collect like terms and get $x^2+x-2=0$. This equation factors as $(x+2)(x-1)=0$, so the two roots are $x=-2$ and $x=1$. The absolute difference of these roots is $|-2-1|=\boxed{3}$.