Scary Limit

Calculus Level 4

$\large\varphi = \displaystyle\lim_{x\rightarrow 0} \dfrac{\alpha - \sqrt{\alpha^2 - x^2} - \dfrac{x^2}{4}}{x^4}, \quad \alpha >0$

If $\varphi$ is finite, then find the value of $\varphi + \alpha$ correct up to 4 decimal places.