Final answer:
To complete the square for the equation x² = 6x + 1, move the constant term to the left, find the value to create a perfect square trinomial and add it to both sides, which results in (x - 3)² = 10.
Step-by-step explanation:
To rewrite the equation x² = 6x + 1 by completing the square, we first need to move the constant term to the other side of the equation:
x² - 6x = 1
Next, we need to find a number that, when added to both sides, completes the square on the left side. We take the coefficient of x, which is -6, divide it by 2, and square it to get (6/2)² = 9.
Add 9 to both sides:
x² - 6x + 9 = 1 + 9
Now, the left side is a perfect square trinomial, and the equation simplifies to:
(x - 3)² = 10
The equation is now in the desired form of (x - a)² = b, specifically:
(x - 3)² = 10