One. (20 points) Let the constant $a \geqslant 0$. Solve the equation $x^{4}+6 x^{3}+(9-2 a) x^{2}-6 a x+a^{2}-4=0$ for $x$.


$$
\begin{array}{l}
a^{2}-\left(2 x^{2}+6 x\right) a+x^{4}+6 x^{3}+9 x^{2}-4=0 \\
\Rightarrow a^{2}-\left(2 x^{2}+6 x\right) a+\left(x^{2}+3 x\right)^{2}-4=0 \\
\Rightarrow a^{2}-\left[\left(x^{2}+3 x+2\right)+\left(x^{2}+3 x-2\right)\right] a+ \\
\quad\left(x^{2}+3 x+2\right)\left(x^{2}+3 x-2\right)=0 \\
\Rightarrow a=x^{2}+3 x+2 \text { and } a=x^{2}+3 x-2 .
\end{array}
$$

Solving respectively, we get
$$
x_{1,2}=\frac{-3 \pm \sqrt{4 a+1}}{2}, x_{3,4}=\frac{-3 \pm \sqrt{4 a+17}}{2} .
$$