Question 1113035
The distance between points {{{A(x,-2)}}} and {{{B(-2,-14)}}} is
{{{d=sqrt((x[A]-x[B])^2+(y[A]-y[B])^2)}}}{{{"="}}}{{{sqrt((x-(-2))^2+((-2)-(-14))^2)}}}{{{"="}}}{{{sqrt((x+2)^2+(-2+14)^2)=sqrt((x^2+4x+4)+12^2)}}}{{{"="}}}{{{sqrt((x+2)^2+144)}}}
You want to find the values for {{{x}}} that make that distance {{{13}}} ,
so you want to solve
{{{sqrt((x+2)^2+144)=13}}} or {{{(x+2)^2+144=13^2}}} or {{{(x+2)^2+144=169}}} . 
 
{{{(x+2)^2+144=169}}}
{{{(x+2)^2=169-144}}}
{{{(x+2)^2=25}}}
{{{x+2=" " +- 5}}}
The solution is
{{{system(x=-2-5,"or",x=-2+5)}}} or {{{highlight(system(x=-7,"or",x=3))}}} .
There are two solutions because point {{{B(-2,-14)}}}
is less than 13 units away from the line {{{y=-2}}} :
{{{drawing(300,300,-14,6,-16,4,grid(0),
red(circle(-2,-14,0.2)),locate(-1.8,-14,red(B)),
green(line(-14,-2,7,-2)),locate(-13.8,-2,green(y=-2)),
circle(-7,-2,0.2),circle(3,-2,0.2),
red(circle(-2,-14,13)),locate(-7.6,-9.4,red(13)),
red(arrow(-6.596,-9.405,-2,-14)),red(arrow(-6.596,-9.405,-11.191,-4.809))
)}}}