In the solution they have done using work energy theorem. cant this be done using force balancing at equilibrium? i'm not getting correct answer using force bal

Consider the system as shown in figure, with two equal masses m and a spring with spring constant k. The coefficient of kinetic friction between the left mass and table is u =and the pulley is frictionless. The system is held with the spring at its natural length and then released. When the masses come to rest, after they are released the spring is stretched to length of x, = k , The value of a is [Answer upto one decimal place] w- m T 4=1/4 m Using work energy theorem. the masses stop when the total work done is zero, since the speed is zero at both initial and final point. Let x be the stretched distance. then we have using conservation of energy, mgx=k +umgr