VTMO 2014 — Grade 9 — semifinal Question 3

Let $x _{1} , x _{2}$ be the roots of $\left(x + 1\right) \left(2 x - 3\right) + \left(x - 4\right) \left(x + 11\right) + 38 = 0$. Find $x _{1}^{2} + x _{2}^{2}$.