https://file.aiquickdraw.com/mathbot/file/1730125001137uaqqqtpa.jpg

To make the expression \( x^2 + 16x \) a perfect-square trinomial, we need to add a constant that completes the square.

Here's the process:

1. **Take half of the coefficient of \( x \)**: The coefficient of \( x \) is 16, so half of 16 is 8.
2. **Square the result**: \( 8^2 = 64 \).

So, adding **64** to \( x^2 + 16x \) will make it a perfect-square trinomial:
\[
x^2 + 16x + 64 = (x + 8)^2
\]

### Answer:
The correct answer is **64**.

Would you like more details on completing the square? 

### Related Questions
1. What is a perfect-square trinomial, and how can it be identified?
2. How does completing the square help solve quadratic equations?
3. Can you create a perfect-square trinomial with any quadratic expression?
4. How is completing the square used in deriving the quadratic formula?
5. What is the general formula for finding the term needed to complete the square?

### Tip
When completing the square, remember to always take half of the coefficient of \( x \) and then square it to find the necessary constant.

Which value must be added to the expression x^2 + 16x to make it a perfect-square trinomial?

Learn how to make x^2 + 16x a perfect-square trinomial by finding the value to add. This algebra problem teaches completing the square, a key concept in quadratic equations. Suitable for Grades 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation