SMO 2011 Senior Round 1 Question 31

In the diagram, $ABCD$ is a quadrilateral such that $\angle ABC=135^\circ$ and $\angle BCD=120^\circ$. Moreover, $AB=2\sqrt3\text{ cm}$, $BC=4-2\sqrt2\text{ cm}$, $CD=4\sqrt2\text{ cm}$ and $AD=x\text{ cm}$. Find $x^2-4x$.