To solve the equation:

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

### Step 1: Factoring the equation
Notice that the quadratic expression can be factored:

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

Thus, the equation is equivalent to:

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

### Step 2: Solve for x
To solve \((x - 1)^2 = 0\), take the square root of both sides:

\[
x - 1 = 0
\]

So:

\[
x = 1
\]

### Solution
The solution to the equation is:

\[
x = 1
\]

Would you like more details on the factoring process or have any other questions? Here are five related questions to deepen your understanding:

1. What is the general method for factoring quadratic equations?
2. How can the quadratic formula be used to solve \(x^2 - 2x + 1 = 0\)?
3. What does it mean when a quadratic equation has a "double root"?
4. How do you determine the number of solutions a quadratic equation has?
5. What are some real-life applications of solving quadratic equations?

**Tip:** If the discriminant of a quadratic equation (\(b^2 - 4ac\)) is zero, it indicates the equation has a **double root**. This means there is exactly one solution, but it's counted twice.

Learn how to solve the quadratic equation x^2 - 2x + 1 = 0 using factoring. This solution explains algebraic concepts, the zero product property, and the factoring of perfect square trinomials, ideal for students in Grades 7-9.

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