How do you complete the square?

You start off with a formula in the form y = x² + bx. The first step is to add the square of half of the coefficient of x: (b/2)². This allows us to rearrange the formula into (x+ b/2)² . However, our formula is not equal to what we started with since we added (b/2)² so we have to subtract it from the end. If the formula you start with has a constant (a term without the variable x) you ignore it in order to rearrange the x² +bx part and then add it back on at the end as it will combine with the (b/2)² term we subtracted.