To complete the square for the quadratic polynomial \( g^2 - 28g \), we want to find a number that makes it a perfect square.
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Start with the quadratic: \[ g^2 - 28g \]
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Take the coefficient of the \( g \) term, which is \(-28\), divide it by 2, and then square it: \[ \left(-\frac{28}{2}\right)^2 = (-14)^2 = 196 \]
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Add this number (196) to the polynomial: \[ g^2 - 28g + 196 \]
Thus, the number that makes the polynomial a perfect-square quadratic is 196.
The completed square form is: \[ (g - 14)^2 \]