Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

g2 − 28g +

1 answer

To complete the square for the quadratic polynomial \( g^2 - 28g \), we want to find a number that makes it a perfect square.

  1. Start with the quadratic: \[ g^2 - 28g \]

  2. Take the coefficient of the \( g \) term, which is \(-28\), divide it by 2, and then square it: \[ \left(-\frac{28}{2}\right)^2 = (-14)^2 = 196 \]

  3. 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: \[ (g - 14)^2 \]