Question 438760
{{{x^2 - 9 = 12 - sqrt(x^2-9)}}}

<==> {{{(x^2 - 9) + sqrt(x^2 - 9) - 12 = 0}}}

<==> {{{(sqrt(x^2 - 9))^2 + sqrt(x^2 - 9) - 12 = 0}}}

<==> {{{(sqrt(x^2 - 9) + 4)(sqrt(x^2 - 9) - 3) = 0}}}

==> {{{sqrt(x^2 - 9) - 3 = 0}}} ==> {{{sqrt(x^2 - 9) = 3}}}
==> {{{x^2 - 9 = 9}}} ==> {{{x^2 = 18}}} ==> {{{x = 3sqrt(2)}}},  {{{-3sqrt(2)}}}.
These two values satisfy the original equation, and so are the final answers.

(Note that we don't get real solutions from the equation {{{sqrt(x^2 - 9) + 4 = 0}}}.