To complete the square for the quadratic polynomial \( q^2 + 26q \), we need to find a number that will make it a perfect square.
- Start with the coefficient of \( q \), which is 26.
- Take half of this coefficient: \( \frac{26}{2} = 13 \).
- Square it: \( 13^2 = 169 \).
Now, we can rewrite the polynomial:
\[ q^2 + 26q + 169 \]
Thus, the number that makes the polynomial a perfect-square quadratic is 169.
The completed square form is:
\[ (q + 13)^2 \]
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