Variance of following process

Question

I got stuck to find the variance of the following AR(1) process. It looks really simple but I just can't solve it.

The process is

$x_{t+1}$ = a + b$x_{t}$ + c$\sqrt{x_{t}}$$\epsilon_{t+1}$

where $\epsilon_{t+1}$ is normal N(0,1)

This is where I get stuck. In order to calculate the variance, I solve

Var(x) = $b^2$Var(x) + $c^2$Var($\sqrt{x_{t}}$)

Then I am not sure how to compute Var($\sqrt{x_{t}}$)

Any tips or hints would be greatly appreciated!