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

Question

t2 − 20t +

Answer 1

To complete the square for the polynomial \( t^2 - 20t \), you follow these steps:

1. Take the coefficient of \( t \), which is \(-20\).
2. Divide it by 2: \[ \frac{-20}{2} = -10 \]
3. Square this result: \[ (-10)^2 = 100 \]

Now, you can write the polynomial as a perfect square quadratic by adding \( 100 \):

\[ t^2 - 20t + 100 = (t - 10)^2 \]

Thus, the number that makes the polynomial a perfect-square quadratic is \( \boxed{100} \).