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

Question

m2 − 5m +

Answer 1

To complete the square for the expression \( m^2 - 5m \), we can follow these steps:

1. Take the coefficient of \( m \), which is \(-5\).
2. Divide it by 2: \(-5 / 2 = -\frac{5}{2}\).
3. Square the result: \((- \frac{5}{2})^2 = \frac{25}{4}\).

Thus, the number that makes the polynomial a perfect-square quadratic is \(\frac{25}{4}\).

Therefore, the completed square form of the polynomial is:

\[ m^2 - 5m + \frac{25}{4} = \left(m - \frac{5}{2}\right)^2. \]