The distance between the points $(x,21)$ and $(4,7)$ is $10 \sqrt{2}.$ Find the sum of all possible values of $x.$

the sum of all possible values of  x is: 2+6 = 8

Step-by-step explanation:

Assume the two points in your question are:

=> The distance between the points A(x,21) and B(4,7) is  

As we know, the distance of two points can be determined by this formula:

Apply this formula in this situation to find all possible values of x, we have:

=  

<=>

<=>

<=> (4-x) = 2 or (4-x) = -2

<=>  x = 2 or x = 6

=> the sum of all possible values of  x is: 2+6 = 8

the graph on the bottom right