If they have a real solution, quadratic equations can always be solved by using the quadratic formula.
If they have a real solution, quadratic equations can also always be solved by expressing them as . To get to that expression sometimes you have to "complete the square."
Some quadratic equations can be solved by factoring.
<--> can be solved using all the strategies a
listed above.
For example, knowing that we figure that also
so the solutions to are and
We did not even have to "complete the square."
Factoring is also easy if we know that because we jnow that a difference of squares is a special product of the form so and we can re-write as
and if thatr product is zero, one of the factors must be zero, so
either <-->
or <-->
The quadratic formula applied to an equation of the form says that the solutions (if they exist) are given by
In the case of , , and so --> -->
which means or
