To complete the square for the polynomial \( k^2 - 28k \), we follow these steps:
- Take the coefficient of the \( k \) term, which is \(-28\).
- Divide it by \( 2 \):
\[ \frac{-28}{2} = -14 \] - Square the result:
\[ (-14)^2 = 196 \]
Now, we add this square to the polynomial to complete the square:
\[ k^2 - 28k + 196 \]
Thus, the number that you need to fill in to make the polynomial a perfect-square quadratic is \( \boxed{196} \).
The completed square expression is:
\[ (k - 14)^2 \]
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