Distance formula

This problem isn't possible. The shortest possible line segment would be between $(4, -7)$ and $(4, 21)$.

This line segment has a length of 28, which is greater than $16 \sqrt2$, so there are no points that work. 

Find the sum of all possible values of x.

Hello Guest!

$y=\sqrt{(16\sqrt{2})^2-(x-4)^2}-7\\ y=21\\ 21=\sqrt{512-(4-x)^2}-7\\ 28^2=512-16+8x-x^2$

$x^2-8x+286=0\\ x=4\pm\sqrt{16-286}\\ x=4\pm 3i\sqrt{30}$

$x\ne\mathbb R$ | No solution.

  !