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The equation provided is a quadratic equation:

\[
w^2 - 9w + 18 = 0
\]

To solve this, we can use the quadratic formula:

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

Here, \(a = 1\), \(b = -9\), and \(c = 18\).

Let me calculate the solution.The solutions to the quadratic equation \( w^2 - 9w + 18 = 0 \) are:

\[
w_1 = 6 \quad \text{and} \quad w_2 = 3
\]

Would you like further explanation or have any questions?

Here are five related questions:
1. How do we determine if a quadratic equation has real solutions?
2. What is the significance of the discriminant in the quadratic formula?
3. Can a quadratic equation have complex solutions? If yes, under what conditions?
4. How can we factor a quadratic equation if it has real and distinct solutions?
5. What other methods besides the quadratic formula can be used to solve a quadratic equation?

**Tip:** Always check the discriminant first to see if the quadratic has real or complex solutions before proceeding.

Learn how to solve the quadratic equation w² - 9w + 18 using the quadratic formula. This step-by-step explanation covers key algebraic concepts and is suitable for students in Grades 9-10.

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