Final answer:
The maximum distance a spring can be stretched from its unstrained position is given by the elastic potential energy equation U(x) = kx², which becomes x = √(2E/k) when considering the conservation of energy and the absence of kinetic energy at the maximum distance.
Step-by-step explanation:
The algebraic expression for the maximum distance x that the spring can be stretched from its unstrained position without the box moving when it is released is given by the equation for elastic potential energy, which is U(x) = kx². Here, k represents the spring constant, which defines the stiffness of the spring, and x is the displacement of the spring from its unstrained, or equilibrium, position. According to the energy conservation principle, the maximum distance the spring can be stretched corresponds to the point where all the energy in the system is potential energy, with no kinetic energy intervening, which is calculated as x = √(2E/k), where E is the total mechanical energy of the system.