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

Question

z2 + 20z +

Answer 1

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

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

So, we need to add \( 100 \) to the expression.

Thus, the completed expression is:

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

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