To complete the square for the polynomial \( z^2 + 27z \), we need to find a number that makes it a perfect square.
- Take the coefficient of \( z \), which is \( 27 \).
- Divide it by \( 2 \): \( \frac{27}{2} = 13.5 \).
- Square this result: \( (13.5)^2 = 182.25 \).
Thus, the number that you need to add to the polynomial \( z^2 + 27z \) to make it a perfect-square quadratic is \( 182.25 \).
So, the completed expression would be:
\[ z^2 + 27z + 182.25 \]
This can be rewritten as:
\[ (z + 13.5)^2 \]
1 answer