The equation provided is:

$x^2 - 2x + 1 = 0$

This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. Let's start by factoring:

$x^2 - 2x + 1 = (x - 1)(x - 1) = 0$

So, the equation simplifies to:

$(x - 1)^2 = 0$

Therefore, the root of the equation is:

$x = 1$

This equation has one repeated root, meaning the root has multiplicity 2.

Would you like more details on how I factored the equation or any other method?

Here are 5 related questions you might find useful:

1. How do you use the quadratic formula to solve quadratic equations?
2. What is the difference between distinct and repeated roots?
3. Can you explain how to complete the square for quadratic equations?
4. How do you solve more complicated quadratic equations that don't factor easily?
5. What is the geometric interpretation of a quadratic equation with a double root?

Tip: When a quadratic equation has only one root, it means the parabola touches the x-axis at exactly one point (a double root).