Find the value of $\sqrt{12 + \sqrt{12 + \sqrt{12 + \dots}}}$, where the pattern continues forever.

Explanation

1. 01

   Let the value be $x$. The part under the first root after 12 is $x$ itself, so $x = \sqrt{12 + x}$.

2. 02

   Square: $x^2 = 12 + x$, so $x^2 - x - 12 = 0$, i.e. $(x - 4)(x + 3) = 0$.

3. 03

   A square root is positive, so $x = 4$.