The quadratic equation $x^2-5x+5=-4x+7$ has two roots. Find the absolute difference of these roots.
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 $|-2-1|=\boxed{3}$.
To find the absolute difference of the roots of the quadratic equation, we'll first need to solve the equation and find the values of the roots.
Given the equation: $x^2-5x+5=-4x+7$
Step 1: Bring all the terms to one side of the equation
$x^2 - 5x + 4x - 5 - 7 = 0$
Step 2: Simplify
$x^2 - x - 12 = 0$
Step 3: Factor the quadratic equation or use the quadratic formula to find the roots.
Factoring method:
$(x - 4)(x + 3) = 0$
Setting each factor to zero, we get:
$x - 4 = 0$ or $x + 3 = 0$
Solving these equations, we find:
$x = 4$ or $x = -3$
Step 4: Find the absolute difference of the two roots
The absolute difference of the roots is $|4 - (-3)| = |7| = \boxed{7}$.