Solve for x...

square root x+16=2+square root x+4.

I tried doing this problem and got 7/3. and i know that is really wrong. can anyone please show me the steps to doing this problem. thanks:)

√(x+16) = 2 + √(x+4)

square both sides

x+16 = 4 + 4√(x+4) + x+4
8 = 4√(x+4)
2 = √(x+4) square again
4 = x+4
x = 0

test it in the original equation.