The given equation is:

\[
x^2 - 8x + 16 = 0
\]

This is a quadratic equation of the form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = -8 \), and \( c = 16 \).

We can solve this using factoring, completing the square, or the quadratic formula. Let's try factoring:

The equation can be factored as:

\[
(x - 4)(x - 4) = 0
\]

This simplifies to:

\[
(x - 4)^2 = 0
\]

So, the solution is:

\[
x = 4
\]

This quadratic has a repeated root, meaning the solution is \( x = 4 \).

Would you like a detailed explanation of factoring or another method for solving this?

Here are five related questions to explore further:

1. What are the steps for factoring a quadratic equation?
2. How would you solve the same equation using the quadratic formula?
3. What is the geometric interpretation of a quadratic equation with a repeated root?
4. How can we complete the square for the equation \( x^2 - 8x + 16 = 0 \)?
5. How do discriminants help determine the nature of roots in a quadratic equation?

**Tip:** Always check the discriminant \( \Delta = b^2 - 4ac \) in quadratic equations to determine the number of real solutions before solving.

Explore how to solve the quadratic equation x^2 - 8x + 16 = 0 by factoring, with detailed steps and explanations. Learn the connection between factoring, the quadratic formula, and the discriminant. Suitable for students in Grades 8-10.

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