complete the square

Question

X^2 - 2x - 3

Answer 1

This is a Drill!  You set the constant -3  a bit to the right of its usual location: x² - 2x             -3

and into vacated space put +1 because +1 is the square of (½ of the coefficient of x).

So you just added 1, and to compensate, you must subtract 1:

x2 - 2x +1   -3 - 1.

 

The first three terms are GUARANTEED to be a perfect square (of a binomial, by this process), so the final answer is

(x + 1)² -4.  Note how the constant at the end has changed.