Final answer:
The value of x for the point (x, 4) to be equidistant from the points (5, -2) and (3, 4) is found to be x = 4 using the distance formula and solving for x.
Step-by-step explanation:
To find the value of x such that the point (x, 4) is equidistant from the points (5, -2) and (3, 4), we can use the distance formula. The distance between two points, (x1, y1) and (x2, y2), is given by √[(x2-x1)^2 + (y2-y1)^2]. Therefore, the distances from (x, 4) to each of the given points must be equal.
We set up two equations based on the distance from (x, 4) to (5, -2) and (3, 4) respectively:
√[(x-5)^2 + (4+2)^2] = √[(x-3)^2 + (4-4)^2]
(x-5)^2 + 36 = (x-3)^2
Solving the second equation, we simplify and find that x = 4. There is no need to form a quadratic equation or use the quadratic formula in this case since the equation simplifies directly and x is not a fraction or a negative value contrary to the misleading example provided.