Why is this incorrect?

Question

I was wondering why a question was incorrect. It says Find the term that must be added to the equation (x^2-2x =3) to make it into a perfect square. I said 4. On my online math test I was marked incorrect on this problem but I don't understand why. 

Answer 1

For perfect square, both sides of the equation should match.

x² - 2x = 3

Adding 1 on both sides, x² - 2x + 1 = 3 +1

(x - 1)² = 4

(x - 1)² = 2²

So adding 1 makes the equation a perfect square.

Answer 2

You were thinking right, but the question was framed wrong. You meant to subtract 3 from both sides and add 4 to make it a perfect square. That is correct. They just jumped a step and added one and got the same result. You should get full points when you explain that to your teacher.