To solve the expression \( a^2 + 12a + (\text{blank}) \), you are most likely trying to complete the square. Completing the square helps rewrite the quadratic expression in a perfect square form, like \( (a + b)^2 \).

Here’s how you do it:

1. Start with the given expression: 
   \[
   a^2 + 12a + (\text{blank})
   \]

2. To complete the square, you take half of the coefficient of the linear term (the term with \(a\)) and square it.
   - The coefficient of \(a\) is \(12\).
   - Half of \(12\) is \(6\).
   - Square \(6\) to get \(36\).

3. The missing term in the blank is \(36\).

So, the completed square form of the expression is:
\[
a^2 + 12a + 36
\]
which can now be factored as:
\[
(a + 6)^2
\]

### Summary:
- The value for the blank is \(36\), and the expression becomes \( (a + 6)^2 \).

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How would you complete the square for \( a^2 + 10a + (\text{blank}) \)?
2. Can you solve \( a^2 + 12a + 36 = 0 \) by factoring?
3. What is the quadratic formula and how does it relate to completing the square?
4. How do you derive the vertex form of a quadratic equation using completing the square?
5. Can completing the square help in solving any quadratic equation?

**Tip:** Completing the square is often used to convert quadratic equations into a form that reveals their vertex and is helpful in solving them graphically!

Explore how to solve the quadratic expression a² + 12a + (blank) by completing the square. This step-by-step guide explains how to determine the missing term (36) and rewrite the expression as (a + 6)². A perfect introduction to quadratic equations for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation