To complete the square for the polynomial \( d^2 + 28d \), you need to add and subtract a specific number that will turn it into a perfect square.
The formula to complete the square is:
\[ \left( \frac{b}{2} \right)^2 \]
where \( b \) is the coefficient of the linear term, which in this case is \( 28 \).
- Compute \( \frac{28}{2} = 14 \).
- Square this result: \( 14^2 = 196 \).
Thus, you need to fill in the blank with \( 196 \). The completed square form of the polynomial is:
\[ d^2 + 28d + 196 = (d + 14)^2. \]
So the final answer is:
196.
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