Inequality problem

Using distance formula,

\(\sqrt{(x-4)^2 + 196} = 10\sqrt{3}\)

Square both sides and subtract 196 on both sides,

\((x-4)^2 + 196 = 300\)

\((x-4)^2 = 104\)

Expand left side and subtract 104 on both sides,

\(x^2 - 8x +16 = 104\)

\(x^2 - 8x -88 = 0\)

Apply quadratic formula to get x values of,

\(x=4±2\sqrt{26}\)

Add both possible values of x together,

\((4+2\sqrt{26}) + (4-2\sqrt{26}) = 8\)

So the final answer is 8.

(10sqrt(3))^2 = (21-7)^2 + (4-x)^2

You can get this equation by creating a right triangle on a coordinate plane and using Pythagorean Theorum. 

300 = 14^2 + (4-x)^2

 

Can you take it from here?

 

=^._.^=