Question
What value of p completes the square in the expression x squared minus 14 x plus p?
(1 point)
Responses
7
7
14
14
49
49
56
(1 point)
Responses
7
7
14
14
49
49
56
Answers
GPT-4o mini
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**
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**