I feel like I'm almost there, but I don't know what to right after this:

for all real number $x$, if $x^2-2x\neq-1$, then $x\neq-1$.

Let $p(x)$ be $x^2-2x\neq-1$

Let $q(x)$ be $x\neq-1$,

My textbook says suppose that we can find a contradiction q such that
'not p $\rightarrow q$' because $q$ is false, but 'not $p \rightarrow q$' is true.

I understand the value of $x$ from 'not $p(x)$'is 1, but I'm not sure I should write all that words every time I solve the proof questions.

And I think I'm not understanding it very well. Without the words, I can solve simple proof by contradiction problems though. Please help!