Answer:
To solve the quadratic equation x^2 - 2x + 1 = 0, we can either factorize the equation or use the quadratic formula.
**Factoring Approach:**
We can rewrite the quadratic equation as:
x^2 - 2x + 1 = (x - 1)(x - 1) = (x - 1)^2
Setting (x - 1)^2 = 0 implies:
x - 1 = 0
x = 1
**Using the Quadratic Formula:**
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
where a = 1, b = -2, and c = 1. Plugging these into the formula, we get:
x = (-(-2) ± sqrt((-2)^2 - 4 * 1 * 1)) / (2 * 1)
x = (2 ± sqrt(4 - 4)) / 2
x = (2 ± 0) / 2
x = 1
**Conclusion:**
In both approaches, the solution is x = 1. This is a double root, meaning the quadratic has a perfect square form and touches the x-axis at this point only.
Step-by-step explanation:
