Question

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

q2 + 20q +

Answer 1

To complete the square for the expression \( q^2 + 20q \), we need to find the number that makes it a perfect-square quadratic.

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

Thus, the number we need to add to \( q^2 + 20q \) to complete the square is \( 100 \).

Therefore, we rewrite the expression as:

\[ q^2 + 20q + 100 \]

This simplifies to:

\[ (q + 10)^2 \]

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