There is always a systematic approach to answering questions that require you to complete the square. Before you start answering the question make sure the coefficient of x^2 is 1. For this particular example that is the case. Now you square root the x^2, then drag down the sign, halve the coefficient of x and then square it all. (This is easier to demonstrate with a whiteboard). So from x² + 2x you end up with: (x + 1)². After this you always put a minus sign and square the number in the bracket (in this example you are doing 1²). You then drag down the number at the end of the question (-6). So you now have: (x + 1)²-1-6. From here you simplify as much as possible giving you the final answer (x + 1)²-7. You can use this approach for all questions involving completing the square. In some cases you have a coefficient of x² that is not equal to 1, there are a few extra steps before you can use this approach.

find f'(x) of (x^2) + 3x + 2.

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