Let the mean and the variance of 20 observations x_1, x_2, …, x_20 be 15 and 9, respectively. For α ∈ R, if the mean of (x_1+α)^2,(x_2+α)^2,…

Let the mean and the variance of $\displaystyle 20$ observations $\displaystyle x_1, x_2, \ldots, x_{20}$ be $\displaystyle 15$ and $\displaystyle 9$, respectively. For $\displaystyle \alpha \in \mathbf{R}$, if the mean of $\displaystyle \left(x_1+\alpha\right)^2,\left(x_2+\alpha\right)^2, \ldots,\left(x_{20}+\alpha\right)^2$ is $\displaystyle 178$, then the square of the maximum value of $\displaystyle \alpha$ is equal to \_\_\_\_.