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

Question

d2 + 19d +

Answer 1

To complete the square for the polynomial \(d^2 + 19d\), we follow these steps:

1. Take the coefficient of \(d\), which is 19.
2. Divide it by 2: \(\frac{19}{2} = 9.5\).
3. Square this result: \((9.5)^2 = 90.25\).

Thus, we need to add 90.25 to the polynomial to make it a perfect square. Therefore, the expression becomes:

\[ d^2 + 19d + 90.25 = (d + 9.5)^2 \]

So, the number that makes the polynomial a perfect-square quadratic is \(90.25\).