<s>[INST] How to solve the equation $t = \sqrt{x^2 - 1} - x$ for $x$? 
Let the equation $t = \sqrt {x^2 - 1} - x$. Find $x$.

So I've tried the following:
$$t^2 = x^2 - 1 -2\sqrt {x^2-1}x + x^2 = 2x^2 - 2\sqrt{x^2-1}x - 1 $$
What should I do next?
 [/INST] The following should be better :
$$\sqrt{x^2-1}=t+x\quad\Rightarrow\quad x^2-1=(t+x)^2$$
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