Answer
x = 4
Work Step by Step
f(x)=g(x) (Solve for x)
$\sqrt x -4 = 2-x$
$\sqrt x=6-x$
$x = x^2 -12x + 36$
$x^2-13x+36=0$
(x-9)(x-4)=0
x = 9 or 4
Plug in the solutions in the original equation to verify the solution
for x = 9
LHS = $\sqrt 9 -4 = 3-4=-1$
$RHS = 2-9 = -7$ not correct
for x = 4
LHS = $\sqrt 4 -4 = 2-4=-2$
RHS = 2-4 = -2
LHS=RHS hence x = 4 is a valid solution
