Question

What is the sum of all possible real values of x, such that there exists a real value y which satisfies the equation (x+y−40)^2+(x−y−18)^2=0?

Answer 1

since all squares are >= 0, both squared expressions must be zero. So you need

x+y-40 = 0 and
x-y-18 = 0

2x-58 = 0
x = 29
y = 11

Only one real value for x satisfies the equation