equation

Solve the equation.

Hello Guest!

$x + \sqrt{x - 2} = 4\\ \sqrt{x - 2} = 4-x\\ x-2=x^2-8x+16\\ x^2-9x+18=0\\ x=4.5\pm \sqrt{4.5^2-18}\\ x=4.5\pm 1.5\\ \color{blue}x\in\{3,6\}$

  !

x = 6 doesn't seem to work.