For what value of m is the equation true?

x^{2} + 10x+11 = m + (x=5) ^2-25

We are given the equation:

x^2 + 10x + 11 = m + (x-5) ^2 - 25

To determine the value of m, assign a value of x and solve for m

if x = 1, the equation becomes

1^2 + 10 (1) + 11 = m + (1 - 5) ^2 - 25

solve for m

m = 31

When m = 31, the equation is true.