How to solve $\sqrt {1+\sqrt {4+\sqrt {16+\sqrt {64+\sqrt {256\ldots }}}}}$ How to solve this equation?

$$x=\sqrt {1+\sqrt {4+\sqrt {16+\sqrt {64+\sqrt {256\ldots }}}}}.$$

Answer: $x=2$
I found this answer.Is that wrong ?
$x^2 = 1 + 2 x$

$x^2 - 2x - 1 = 0$

$x = 1 + \sqrt{2}$ because $x &gt; 0$.