A quadratic equation is a statement with a variable in it that's raised to the second power, or squared, and there aren't any variables in the statement that have a higher power than that. If the equation is quadratic, it may have two solutions, one solution, or no solutions at all. You can solve a quadratic equation with four possible methods:
- BGBG: By Guess or By Golly — This isn't very efficient, but sometimes solutions seem obvious, and there's no harm in recognizing or knowing the solution!
- Factoring — This is probably the most efficient way of solving a quadratic equation — as long as the solutions are rational numbers, which means it's factorable.
- Quadratic Formula — The quadratic formula always works. Whether an equation factors or not, you can always use the quadratic formula to get the answers. When isn't it always used then? The quadratic formula can be rather messy and cumbersome, and you can make errors more easily during this method than by factoring. This formula is your second resort.
- Completing the Square — This method should never be used to solve a quadratic equation. However, students are asked to do just that. Completing the square is an important technique used to rewrite equations of circles, parabolas, hyperbolas, and ellipses in their standard form — a more useful form. By learning completing the square as a method of solving quadratics, you get practice for later. And, this method does give the answers to the problems.