What value of p completes the square in the expression x squared minus 14 x plus p?

Question

(1 point)
Responses

7
7

14
14

49
49

56

Answer 1

To complete the square for the expression \( x^2 - 14x + p \), we will focus on the \( x^2 - 14x \) part first.

1. Take the coefficient of \( x \), which is \(-14\), and divide it by 2:
   \[ \frac{-14}{2} = -7 \]

2. Next, square this result:
   \[ (-7)^2 = 49 \]

3. This means that to complete the square, we need to add \( 49 \) to \( p \). Therefore, the expression can be rewritten as:
   \[ x^2 - 14x + 49 - 49 + p = (x - 7)^2 + (p - 49) \]

To complete the square, we set \( p \) to \( 49 \).

Thus, the value of \( p \) that completes the square is \( 49 \).

The correct response is: 49