Following up my previous post that gave you advice on how to solve equations, in this post I would like to go over some strategies on how to solve quadratic equations. Quadratic equations become very common in high school math and college math, and they require a bit more work sometimes to solve. You may already have experience using the quadratic formula, which I will explain shortly and is extraordinarily good to memorize! First though, let’s go over solving quadratic equations. To do this, you will commonly rely on factoring quadratics techniques. You can refer to my previous post on methods of factoring for some additional tips!
When most students hear “quadratic equation,” they usually get anxious because quite often this means having to work with the quadratic formula. This formula is more complicated than most that you have probably encountered up to this point, but factoring quadratics doesn’t always rely on the quadratic formula! In fact, they can be quite simple! A quadratic equation isn’t just “something that needs the quadratic formula” to solve it. Quite simply, a quadratic equation is just an equation that can written in this form:
ax2 + bx + c = 0 where a, b, and c are real numbers and a does not equal 0
See? That doesn’t sound so bad. The KEY is that the “a” value is not 0. b and c can be, but not a. You need to have the x2 term.
Remember, “solving an equation” means to find the roots or solution… or, what makes the expression true? To do this with quadratic equations, we rely on the property that says “two terms multiplied = 0 only if one or both of those terms is 0.” Remember this property! It is key to the quadratic factoring method. If we combine this property with our ‘grouping’ factoring method, you will see how this all comes together.
