Final answer:
To transform the polynomial x²-2x=3 into a perfect square, we need to add a constant term to both sides of the equation. We can do this by adding the square of half the coefficient of the x-term to both sides. The final equation is (x-1)²=4.
Step-by-step explanation:
To transform the polynomial x²-2x=3 into a perfect square, we need to add a constant term to both sides of the equation. We can do this by adding the square of half the coefficient of the x-term to both sides. In this case, the coefficient of the x-term is -2, so half of it is -1. The square of -1 is 1. Adding 1 to both sides of the equation, we get x²-2x+1=4. Now, the left side of the equation is a perfect square. We can rewrite it as (x-1)²=4.