# How do you simplify x=sqrt( 6-x)?

First we notice that it should be $6 - x \ge 0 \implies 6 \ge x$ and $x \ge 0$ hence $0 \le x \le 6$
$x = \sqrt{6 - x} \implies {x}^{2} = 6 - x \implies {x}^{2} + x - 6 = 0 \implies \left(x - 2\right) \cdot \left(x + 3\right) = 0$
Hence the only acceptable solution is $x = 2$