Final answer:
The quadratic equation x^2-2x+1=9 is solved by completing the square, resulting in the two solutions x=4 and x=-2.
Step-by-step explanation:
To solve the given equation x^2-2x+1=9 by completing the square, we can follow these steps:
- First, move the constant term to the other side of the equation: x^2 - 2x = 8.
- Next, complete the square on the left side by adding and subtracting the square of half the coefficient of x, which is 1, giving us: x^2 - 2x + 1 = 8 + 1.
- Now, recognize the left side as a perfect square: (x - 1)^2 = 9.
- Take the square root of both sides of the equation, remembering to consider both the positive and negative square roots: x-1 = ±3.
- Finally, solve for x by adding 1 to both sides: x = 1 ± 3. So, the two solutions for x are x = 4 and x = -2.
By following these steps, we have completed the square and found the solutions to the equation x^2-2x+1=9.