To complete the square for the quadratic expression \(x^2 - 22x\), we need to find a constant that makes it a perfect square trinomial.
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Take the coefficient of \(x\) (which is \(-22\)), divide it by 2, and then square the result: \[ \left(\frac{-22}{2}\right)^2 = (-11)^2 = 121 \]
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Now, add this value (121) to the expression: \[ x^2 - 22x + 121 \]
Thus, the completed square form is: \[ (x - 11)^2 \]
Therefore, the number you need to fill in to make the polynomial a perfect-square quadratic is 121.
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