Answer
$x= 0.292m$
Work Step by Step
The initial kinetic energy is equal to the final spring and thermal energy
$K = E_s + E_{th}$
$K = \frac{1}{2}kx^2+ fx$
$20 = \frac{1}{2}400x^2+ 10x$
$0 = 200x^2+ 10x -20$
$0 = 20x^2+ x -2$
Solving the equation with a calculator/wolfram alpha:
$x= 0.292m$
