the length of a segment with coordinates (-1, 4) and (x, 0) is 5,what is x?
Use Pythagoras to get the length of the segment as
$$\sqrt{(x--1)^2+(0-4)^2}=\sqrt{(x+1)^2+16}$$ So we must have
$$\sqrt{(x+1)^2+16}=5$$or
$$(x+1)^2+16=25\\\\ (x+1)^2=9\\\\ x+1=\pm3\\\\ x=\pm3-1$$so x = 2 and x = -4.
