Answer
$x=16$
Work Step by Step
$\sqrt {x+9} =2+\sqrt {x-7}$
$(\sqrt {x+9})^2 =(2+\sqrt {x-7})^2$
$x+9 = 2*2+2(\sqrt {x-7})+2(\sqrt {x-7})+\sqrt {x-7}*\sqrt {x-7}$
$x+9 = 4+4(\sqrt {x-7})+(x-7)$
$x+9 = x-3+4\sqrt {x-7}$
$9 = -3+4\sqrt {x-7}$
$12 = 4\sqrt {x-7}$
$12/4 = 4\sqrt {x-7}/4$
$3= \sqrt {x-7}$
$3^2= (\sqrt {x-7})^2$
$9=x-7$
$16=x$
$\sqrt {x+9} =2+\sqrt {x-7}$
$\sqrt {16+9} =2+\sqrt {16-7}$
$\sqrt {25} =2+\sqrt {9}$
$5=2+3$
$5=5$ (true)
