bounding $(|\alpha|+1)^2+(x+|\alpha|)^2$

Question

Let $x>0$ and $\alpha\in\mathbb{R}$ be a 'parameter'. If possible, I would like to find an upper bound for the quantity $(|\alpha|+1)^2+(x+|\alpha|)^2$. All ideas are welcome. If there's an inequality one can use, that would be great. All I'm able to show at this point is that $(|\alpha|+1)^2+(x+|\alpha|)^2\geq 8|\alpha|\sqrt{x}$.