When a Is Not 1

The pattern (x + p)^2 = x^2 + 2px + p^2 always starts with a plain x^2. So completing the square this way needs the coefficient of x^2 to be 1.

The fix is one step. Take 2x^2 - 4x - 6 = 0. Divide both sides by 2: x^2 - 2x - 3 = 0. Nothing is lost, because dividing both sides by the same nonzero number keeps every solution. Now complete the square as usual: (x - 1)^2 = 4, so x is 3 or -1.

Divide every term, including the number on the right. Here that number is 0, and 0 divided by 2 stays 0, which is why the equation keeps its zero.