2. When $x=\frac{\sqrt{29}-3}{2}$, the value of the algebraic expression
$$
x^{4}+5 x^{3}-3 x^{2}-8 x+9
$$

is $\qquad$.
$2.7 \sqrt{29}-32$.
Since $x=\frac{\sqrt{29}-3}{2}$ is a root of the equation $x^{2}+3 x-5=0$, then
$$
\begin{array}{l}
x^{4}+5 x^{3}-3 x^{2}-8 x+9 \\
=\left(x^{2}+3 x-5\right)\left(x^{2}+2 x-4\right)+14 x-11 \\
=14 x-11=14 \times \frac{\sqrt{29}-3}{2}-11=7 \sqrt{29}-32 .
\end{array}
$$