Question

By completing the square, the expression x^2 + 2x + 63 equals (x + A)^2 + B, where A = ___ and B = ___.

a) A=1,B=64
b)A=1,B=62
c) A=2,B=65
d) A=2,B=61

Answer 1

By completing the square for the expression x^2 + 2x + 63, we find that it equals (x + 1)^2 + 62, thus A = 1 and B = 62, following the standard process of completing the square.

Step-by-step explanation:

To complete the square for the given expression x^2 + 2x + 63, we follow these steps:

1. Identify the coefficient of the linear term, which is 2.
2. Divide this coefficient by 2 to obtain 1, and then square it to get 12 = 1.
3. Add and subtract this square within the expression to get x^2 + 2x + 1 - 1 + 63.
4. Now, we can rewrite the expression as (x+1)^2 + 62.
5. This matches the form (x + A)^2 + B, where A = 1 and B = 62.

Therefore, A = 1 and B = 62, which corresponds to option b) A=1, B=62.