The function $\displaystyle f$ is defined by $\displaystyle f(x)=ln[(x-1)^2-k]$, where $\displaystyle x<-2$ and $\displaystyle k$ is a constant. Find the maximum value of $\displaystyle k$.

what i did was:

$\displaystyle [(x-1)^2-k]>0$ but since there're two unknowns, i couldn't solve it