Let $a, b \in \mathbb{R}$, $a \neq 0$ be such that the equation $ax^2 - 2bx + 5 = 0$ has a repeated root $\alpha$, which is also a root of the equation $x^2 - 2bx - 10 = 0$. If $\beta$ is the other root of this equation, then $\alpha^2 + \beta^2$ is equal to: