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Let $P = \begin{bmatrix} 3 & -1 & -2 \ 2 & 0 & \alpha \ 3 & -5 & 0 \end{bmatrix}$, where $\alpha \in R$. Suppose $Q = [q_{ij}]$ is a matrix satisfying $PQ = kI_3$ for some non-zero $k \in R$. If $q_{23} = -\dfrac{k}{8}$ and $|Q| = \dfrac{k^2}{2}$, then $\alpha^2 + k^2$ is equal to ______.
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