$(x-4)^2+8|x-4|+15=0$

Question

The sum of the roots of the equation $(x-4)^2+8|x-4|+15=0$ is

My attempt: Let $|x-4|=y$. So, the equation becomes $y^2+8y+15=0$. So, $y=-3,-5$. Both values should be rejected as $|x-4|$ cannot be negative. But the answer has been given as $16$.

Answer 1

Since the answer has been given as $16$, I think that the equation should read

$$(x-4)^2-8|x-4|+15=0.$$

Now let $y:=|x-4|$ and proceed as above.