To factor and solve the quadratic equation \( x^2 - 16x + 54 = 0 \), let's follow these steps:

### 1. Factor the quadratic expression:
We are looking for two numbers that multiply to give the constant term \( 54 \) and add up to the coefficient of \( x \), which is \( -16 \).

- The two numbers are \( -9 \) and \( -6 \), since:
  \[
  -9 \times -6 = 54 \quad \text{and} \quad -9 + -6 = -16
  \]

So, we can factor the quadratic as:
\[
x^2 - 16x + 54 = (x - 9)(x - 6) = 0
\]

### 2. Solve for \( x \):
Set each factor equal to zero:
\[
x - 9 = 0 \quad \text{or} \quad x - 6 = 0
\]
Solving these gives:
\[
x = 9 \quad \text{or} \quad x = 6
\]

### Final Answer:
The solutions to the equation are:
\[
x = 9 \quad \text{or} \quad x = 6
\]

Would you like more details or have any questions?

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Here are 5 related questions you might find useful:
1. How do you solve quadratic equations using the quadratic formula?
2. What are other methods to solve quadratic equations besides factoring?
3. How can you verify the solutions of a quadratic equation?
4. What is the relationship between the discriminant and the nature of the roots of a quadratic equation?
5. How would you solve \(x^2 - 16x + 60 = 0\)?

**Tip:** Always check your factorization by expanding the factors to see if they match the original quadratic equation!

Learn how to factor and solve the quadratic equation x^2 - 16x + 54 = 0. This step-by-step solution demonstrates how to find the factors and solve using the zero product property. Suitable for students in Grades 8-10.

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