I am wondering how Gali derived equation (25) in chapter 5 of his book Monetary Policy, Inflation, and the Business Cycle (2015).
We have equation (21): $$ \vartheta \hat{x}_{t} = -\kappa \hat{p}_{t} + \Lambda $$ and equation (23): $$ \hat{p}_{t} = \delta\hat{p}_{t-1} + \frac{\delta}{1-\delta\beta\rho_u}u_{t} + \frac{\delta}{1-\delta\beta}\frac{\kappa\Lambda}{\vartheta}. $$ Gali then combines (21) and (23) to get (25): $$ \hat{x}_t = \delta\hat{x}_{t-1} - \frac{\kappa\delta}{\vartheta(1-\delta\beta\rho_u)}u_t. $$
Now, unless I've made some kind of silly algebraic mistake, I'm not quite sure how he no longer has a constant term in (25). Or maybe I'm missing a simplifying assumption regarding some of the variables?
If someone can briefly explain this, it would be much appreciated.