A quadratic equation in one variable is an equation of the form , where , and are constants (that is, they do not depend on ) and is the unknown variable. Quadratic equations are solved using one of three main strategies: factoring, completing the square and the quadratic formula.
The purpose of factoring is to turn a general quadratic into a product of binomials. This is easier to illustrate than to describe.
Example: Solve the equation for . Note: This is different for all quadratics; we cleverly chose this so that it has common factors.
First, we expand the middle term: .
Next, we factor out our common terms to get .
We can now factor the term to get . By the zero-product property, either or equals zero.
We now have the pair of equations and . These give us the answers and , which can also be written as . Plugging these back into the original equation, we find that both of these work! We are done.
Completing the square
See Quadratic Formula.