Given the equation:

\[ A + AA = 72 \]

Let's interpret \(AA\) as \(A \times A\). The equation then becomes:

\[ A + A^2 = 72 \]

This is a quadratic equation. Rearranging it into standard form:

\[ A^2 + A - 72 = 0 \]

To solve for \(A\), we can use the quadratic formula:

\[ A = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here, \(a = 1\), \(b = 1\), and \(c = -72\). Plugging these values into the quadratic formula:

\[ A = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot (-72)}}{2 \cdot 1} \]

\[ A = \frac{-1 \pm \sqrt{1 + 288}}{2} \]

\[ A = \frac{-1 \pm \sqrt{289}}{2} \]

\[ A = \frac{-1 \pm 17}{2} \]

This gives us two possible solutions:

\[ A = \frac{-1 + 17}{2} = 8 \]

\[ A = \frac{-1 - 17}{2} = -9 \]

So, the possible values for \(A\) are 8 and -9. Since we usually consider positive solutions in many contexts, the most likely value is:

\[ A = 8 \]

Would you like more details or have any questions? Here are some questions you might ask next:

1. How do you solve other types of quadratic equations?
2. Can you explain why we interpret \(AA\) as \(A \times A\)?
3. What are the real-world applications of solving quadratic equations?
4. Can you solve a quadratic equation using factorization?
5. How do you graph a quadratic equation?

**Tip:** When solving quadratic equations, always check if they can be factored easily before using the quadratic formula for a quicker solution.

Learn how to solve the equation A + AA = 72 using the quadratic formula. Understand the steps involved in solving quadratic equations, interpretation of variables, and choosing the appropriate solution. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation