…wonderful life

Lovely equation

On this weblog I encountered a great equation that can be solved in a creative way (the dots denote that the expression in repeated infinitely). I have reproduced it here:

(I) $\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}=4$

square both sides

(II) ${x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}=16$

now substitute  I in II

$x+4=16$

gives

$x=12$