https://file.aiquickdraw.com/mathbot/file/1727113082451u9t7vkzs.jpg

The problem in the image asks to solve the quadratic equation \( n^2 - 11n + 18 = 0 \) by factoring.

### Solution by factoring:

The general approach is to find two numbers that multiply to give the constant term (18) and add to give the middle coefficient (-11).

We need two numbers whose:
- Product = 18
- Sum = -11

These numbers are -9 and -2, because:
- \(-9 \times -2 = 18\)
- \(-9 + -2 = -11\)

Thus, we can factor the quadratic expression as:

\[
n^2 - 11n + 18 = (n - 9)(n - 2) = 0
\]

To find the solutions, set each factor equal to zero:

\[
n - 9 = 0 \quad \text{or} \quad n - 2 = 0
\]

Thus, the solutions are:

\[
n = 9 \quad \text{or} \quad n = 2
\]

### Final answer:
The values of \( n \) are \( 9 \) and \( 2 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you factor quadratics when the leading coefficient isn't 1?
2. What if the quadratic equation does not factor neatly?
3. How can the quadratic formula be used as an alternative?
4. What is the significance of the discriminant in solving quadratics?
5. How can quadratic equations be applied to real-world problems?

**Tip:** When factoring quadratic equations, always look for pairs of numbers that multiply to the constant and add to the linear coefficient.

Solve the quadratic equation n^2 - 11n + 18 using the factoring method. This detailed guide breaks down the process for students in Grades 7-9, covering key concepts in algebra and quadratic equations.

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