OpenSAT

We can use the following relationship: for a quadratic equation of the form $ax^2 + bx + c = 0$, the sum of the squares of the roots is equal to $\frac{b^2 - 2ac}{a^2}$. In this case, $a = 2$, $b = 5$, and $c = -3$. Therefore, $x_1^2 + x_2^2 = \frac{5^2 - 2(2)(-3)}{2^2} = \frac{25 + 12}{4} = \frac{37}{4}$.