Final answer:
To rewrite the equation 0=x² -6x+1 in the form (x-p)² =q, you need to complete the square. Follow the step-by-step process to move the constant term, calculate and add the square value, and simplify the equation.
Step-by-step explanation:
To rewrite the equation 0=x² -6x+1 in the form (x-p)² =q, we need to complete the square.
Step 1: Move the constant term to the other side of the equation: x² -6x = -1
Step 2: Take half of the coefficient of the x-term (-6) and square it: (-6/2)² = (-3)² = 9
Step 3: Add the value obtained in Step 2 to both sides of the equation: x² -6x + 9 = -1 + 9
Step 4: Simplify and rewrite the equation in the desired form: (x-3)² = 8