The equation you provided is:

\[
x^2 - 2x + 1 = 0
\]

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

### Solution:
We can solve this quadratic equation using factoring, as it can be factored easily:

\[
x^2 - 2x + 1 = (x - 1)(x - 1) = 0
\]

Thus, the equation becomes:

\[
(x - 1)^2 = 0
\]

Solving for \( x \):

\[
x - 1 = 0 \quad \Rightarrow \quad x = 1
\]

### Conclusion:
The solution to the equation \( x^2 - 2x + 1 = 0 \) is:

\[
x = 1
\]

---

Would you like more details on how factoring works here? Or have any other questions? Here are some related questions you can explore:

1. How would you solve a quadratic equation using the quadratic formula?
2. What is the discriminant of a quadratic equation, and how does it affect the solutions?
3. How do you complete the square to solve a quadratic equation?
4. What is the general form of a quadratic equation and its applications?
5. Can a quadratic equation have complex solutions? If so, how?

Tip: Always check if a quadratic can be factored easily before applying more complex methods like the quadratic formula. It saves time!

Discover the step-by-step solution to the quadratic equation x^2 - 2x + 1 = 0, solved by factoring. This approach demonstrates key algebraic methods and factoring techniques, ideal for students in Grades 7-9.

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