Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

Question

w2 + 28w +

Answer 1

To complete the square for the polynomial \( w^2 + 28w \), we follow these steps:

1. Start with the polynomial: \[ w^2 + 28w \]

2. Take the coefficient of \( w \), which is \( 28 \), and divide it by \( 2 \): \[ \frac{28}{2} = 14 \]

3. Square this result: \[ 14^2 = 196 \]

4. The polynomial \( w^2 + 28w \) can be rewritten as: \[ w^2 + 28w + 196 - 196 = (w + 14)^2 - 196 \]

Thus, the number that makes the polynomial a perfect-square quadratic is: \[ \boxed{196} \]

Now the final expression can be written as \( (w + 14)^2 \).