Quadratic equation
A quadratic equation is an equation of the form . a, b, and c are constants, and x is the unknown variable. Quadratic equations are solved using 3 main strategies: factoring, completing the square, and the quadratic formula.
Factoring
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.
Solution:
First, we expand the middle term: .
Next, we factor out our common terms to get .
We can now factor the term to get . By a well known theorem, 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
Quadratic Formula
See Quadratic Formula.