A problem by Breno Linhares

$\sqrt{2+\sqrt{2+...}}=X$ $(\sqrt{2+\sqrt{2+...}})²=X²$ $2+\sqrt{2+\sqrt{2+...}}=X²$ $\sqrt{2+\sqrt{2+...}}=X²-2$ then: $X²-2=X$ $X²-2-X=0$ $X=2 or X=-1$ X is a result of a square root, so that cannot be a negative number, so the answer is $X=2$