By completing the square, the expression x^2+16x+53equals (x+A)^2+B

Question

I need to know how to find the value of A and B, but I dont know how to do that.

Answer 1

Given expression x^2+16x+53 = (x+A)^2+B

To complte squre add (half of x coefficient)^2 and subtract it.

x coefficient is 16, So (half coefficient of x)^2 is 64.

x^2+16x+53+64-64 = (x+A)^2+B

x^2+16x+64+53-64 = (x+A)^2+B

(x+8)^2-11 = (x+A)^2+B

A = 8 and B = -11