For what positive value of m will the following equation be true if n = 5?

(m + n)^2 + (m - n)^2 + m^2 + n^2 = 318.

If n = 5, then m = 9

but how did you do it?

Solve for m: (m - 5)^2 + m^2 + (m + 5)^2 = 293

Expand out terms of the left hand side: 3 m^2 + 50 = 293

Subtract 50 from both sides: 3 m^2 = 243

Divide both sides by 3: m^2 = 81

Take the square root of both sides:

m = 9 or m = -9