Hi Sonia!!!

Here I attempt to explain why these methods are used.

To use the results from the earlier part fully, we need to convert the expression into an equivalent form which contains the result in the earlier part. This method of introducing terms followed by subtracting the same term (or introducing a multiple followed by dividing by the same multiple) is very important in these questions.

In completing the square, recall that we need to introduce a constant term that is equal to the square of half the coefficient of x. So if we have x2 + 6x, then we need into introduce (6/2)^2 = 9 so that x2 + 6x + 9 can be completed into a (x + 3)^2 square. However, we must return the 9 immediately to keep the expression equivalent to before.

So x2 + 6x equals x2 + 6x + 9 - 9 which equals (x + 3)^2 - 9.

Observe how introducing 9 allows us to complete the square.

Similar ideas apply for these questions. Hopefully you get the idea of the workings!