tim age is twice as mitch, the product of their age is 18. write quadratic form

Let's denote Mitch's age as \( m \) and Tim's age as \( t \).

According to the problem:
1. Tim's age is twice Mitch's age:
   \[
   t = 2m
   \]

2. The product of their ages is 18:
   \[
   t \cdot m = 18
   \]

Substituting the first equation into the second equation:
\[
(2m) \cdot m = 18
\]

This simplifies to:
\[
2m^2 = 18
\]

To write this in standard quadratic form, we first move all terms to one side of the equation:
\[
2m^2 - 18 = 0
\]

Next, we simplify the equation by dividing all terms by 2:
\[
m^2 - 9 = 0
\]

The quadratic equation in standard form is:
\[
m^2 - 9 = 0
\]

Would you like details on how to solve this quadratic equation or have any other questions?

Here are some related questions:
1. How do you solve the quadratic equation \(m^2 - 9 = 0\)?
2. What are the roots of the quadratic equation \(m^2 - 9 = 0\)?
3. How would you factorize the equation \(m^2 - 9 = 0\)?
4. What is the significance of the roots in the context of the ages problem?
5. Can the quadratic formula be used to solve \(m^2 - 9 = 0\)?
6. How do you derive the relationship \(t = 2m\) from the given conditions?
7. Are there any real-life scenarios where such a quadratic equation might apply?
8. How can we verify the solution to this quadratic equation?

**Tip:** Quadratic equations often have two solutions, so always check both to see which one fits the context of the problem.

Learn how to solve the quadratic equation m^2 - 9 = 0 with a detailed step-by-step solution. This problem involves finding the ages of Tim and Mitch based on given conditions. Explore the algebraic methods used, including the quadratic equation formula and the relationship between their ages. Suitable for students in Grades 7-9.

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