Problem: By completing the square, the expression x^2+16x+53 equals (x+A)^2+B
I need to know how to find the value of A and B, but I dont know how to do that.
You didn't give us and equation, with a value on the right side. If it is zero:
x^2 + 16x + 53 = 0
x^2 + 16x = -53
x^2 + 16x + 8^2 = -53 + 8^2
(x + 8)^2 = -53 + 64
(x + 8)^2 = 11
(x + 8)^2 - 11 = 0
From this, we can say that A = 8 and B = -11.