The quadratic equation is used to solve a polynomial equation when there is a single variable which is raised to more than one power. Most importantly, the quadratic equation is used when factoring and/or other simplification methods cannot work. For example, consider the following equation:
6x2 + 11x = 35
If you attempt to simplify this equation, you'll notice that the equation is hard to factor, and it would take a long time to find out if there are any whole number factors that can solve the equation. To solve for x, you'll need to use the quadratic equation:
Where a is the coefficient for x2, b is the coefficient for x, and c is the coefficient without the variable.
First rewrite the equation as follows:
6x2 + 11x - 35 = 0
where we see that a = 6, b = 11, and c = -35, and solving the quadratic equation we get:
Which means that there are two possible solutions: one when the plus sign is used and the other when the negative sign is used. The solutions are (-42/12) and (20/12).