Solving Quadratic Equations
If a quadratic equation has a real solution, then its discriminant is nonnegative

If a quadratic equation has a single, but repeating solution, then its discriminant is 0 
If a quadratic equation has a positive discriminant that is a perfect square, then the quadratic equation has a pair of distinct rational solutions that can be found using factoring. 
If a quadratic equation has a positive discriminant that is NOT a perfect square, then the quadratic equation has a pair of distinct irrational solutions that can NOT be found using factoring. 