To complete the square for the polynomial \( x^2 - 22x \), we need to find a number that makes it a perfect-square quadratic.
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Take the coefficient of \( x \), which is \(-22\), and halve it: \[ \frac{-22}{2} = -11. \]
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Then, square this result: \[ (-11)^2 = 121. \]
Therefore, to complete the square, you need to add \( 121 \) to the polynomial.
Thus, the polynomial can be expressed as: \[ x^2 - 22x + 121. \]
This means the number that makes the polynomial a perfect-square quadratic is 121.