How to Solve Quadratic Equations the Quadratic Formula
The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are
Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to show you how to solve quadratic equations using the quadratic formula.Recall that a quadratic equation is an expression made up of a degree two polynomial in a single variable. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are coefficients.Let's take a look at this example. Notice we have a quadratic equation, but it's not in standard form. To get into standard form we have to move all the terms – non-zero terms, that is – to one side of the equal sign. We can do this by subtracting this two from both sides of the equation. That'll give us two x squared, minus three x, minus two, equals zero.Now that we have it in standard form we can identify our a, b, and c. That is, two as our a, negative three is our b, and negative two as our c. We plug that in to our quadratic formula to get two different solutions. We have negative three (quadratic formula – our first term is going to be a negative of the b); plus or minus the square root of b squared – that is, negative three squared; minus four times a, which is two; times c, which is negative two.And, finally, on the denominator we have two times our a, which is just two. We're going to have to do this calculation twice: once with a positive sign, and the other time with a negative sign. It'll give us two different answers: the first answer (if we do plus) is going to be two; the second answer (if we do minus), we'll get negative one-half.Thanks for watching, and to learn more, visit us on the web at About.com.