Set of real numbers such that x²-16x+64=0

The given equation is:

\[
x^2 - 16x + 64 = 0
\]

This is a quadratic equation. To solve it, we can factor it as follows:

\[
x^2 - 16x + 64 = (x - 8)(x - 8) = 0
\]

Thus, the factored form is:

\[
(x - 8)^2 = 0
\]

Setting \( (x - 8) = 0 \), we get:

\[
x = 8
\]

So, the only real solution is \( x = 8 \). Therefore, the set of real numbers that satisfies the equation is:

\[
\{ 8 \}
\]

Would you like a detailed explanation of factoring or quadratic equations?

### Related Questions:
1. How do you factor a quadratic equation?
2. What is the quadratic formula and how is it used?
3. Can a quadratic equation have more than one solution?
4. What are the conditions for a quadratic equation to have real solutions?
5. How do we complete the square to solve quadratic equations?

### Tip: 
Always check for perfect square trinomials like \( x^2 - 16x + 64 \) before using the quadratic formula—they can be factored easily!

Set of real numbers such that x² - 16x + 64 = 0

Learn how to solve the quadratic equation x² - 16x + 64 by factoring. This problem demonstrates the concept of perfect square trinomials and how to find real solutions. Suitable for students in Grades 8-10.

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