What is the x-coordinate of the point on the x-axis that is equidistant from points (-2, 0) and (0, 4)?

Call the point we are looking for  (a, 0)

Since we are equating distances,  we can equate  the distances^2

So

( a - -2)^2  +(0 - 0)^2  = ( a - 0)^2  + (4 - 0)^2     simplify

(a + 2)^2   =  a^2  +  16

a^2 + 4a + 4  = a^2 + 16

4a + 4 =  16

4a  = 12

a =   3 =   the x coordinate we are  looking for