Answer
$x=0$
Work Step by Step
$\sqrt {9+x} =x+3$
$(\sqrt {9+x})^2 =(x+3)^2$
$9+x=x^2+6x+9$
$x=x^2+6x$
$0=x^2+5x$
$0=x(x+5)$
$x=0$
$x+5=0$
$x=-5$
$\sqrt {9+x} =x+3$
$\sqrt {9+0} =0+3$
$\sqrt 9 =3$
$3=3$ (true)
$\sqrt {9+x} =x+3$
$\sqrt {9+(-5)} =-5+3$
$\sqrt 4 =-2$
$2\ne -2$ (false statement)