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.

  !