In this study, we examine dense compact objects, such as white dwarfs and neutron stars, through the lens of Einstein's theory of gravity. Our focus is on understanding these objects when they are not perfectly spherical, using a mathematical description for their gravitational fields. We consider the quadrupole moment as an additional parameter that explicitly enters the equilibrium equations and the geometry of spacetime. In fact, most studies of equilibrium conditions in relativistic astrophysics are limited to the case of spherically symmetric sources. We construct approximate interior and exterior line elements, considering the quadrupole moment up to the first order, to describe static deformed compact objects. We pay particular attention to the interiors of slightly deformed compact objects, applying a specific formula known as the equation of state (EoS). This critical component enables us to understand how these stars balance the force of their own gravity with internal pressure. The EoS is pivotal in determining how matter behaves under the extreme conditions of density and pressure found within these compact objects.