The distance between the points (x,21) and (4,7) is 10sqrt2 Find the sum of all possible values of x.

Use the distance formula:  d  =  sqrt( (x₂ - x₁)² +(y₂ - y₁)² )

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

 

Square both sides:

--->   200  =  (4 - x)² + (-14)²

--->   200  =  (4 - x)² + 196

--->       4  =  (4 - x)² 

 

Find the square root of both sides:

--->     4 - x  =  2          or          4 - x  =  -2

                x  =  2                             x  =  6

 

Etc. ...