![]() The individual steps of this method had been separately discovered by ancient mathematicians. Known thousands of years ago (Babylonians, Greeks) Thus − B 2 ± uwork as rand s, and are all the roots.Two numbers sum to − Bwhen they are − B 2 ± u.If you find rand swith sum − Band product C, then x 2 + B x + C = ( x − r ) ( x − s ), and they are all the roots.Alternative Method of Solving Quadratic Equations One night in September 2019, while brainstorming different ways to think about the quadratic formula, I was surprised to come up with a simple method of eliminating guess-and-check from factoring that I had never seen before. I've recently been systematically thinking about how to explain school math concepts in more thoughtful and interesting ways, while creating my Daily Challenge lessons. ![]() You can reach me through the contact page on my website –. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. Each Wednesday I post an article related to General Teaching on my blog. I am a math instructor at College of the Sequoias in Visalia, CA. I hope that you find this helpful. If you have any questions about solving quadratic equations, or if you have any other topics you are interested in, you can reach me through the contact page at my web site –. The same is true for the quadratic formula. If you have a dirty window, a sledgehammer will clear the view of dirt but it is not the best tool. The quadratic formula can be used to solve any equation, but is often not the best choice. Use the quadratic formula only when none of the previous techniques can be applied efficiently. Solve for x by subtracting 4 from both sides. The same thing occurs when the coefficient of the x-term is odd. ![]() If the leading coefficient is not 1, you must divide through by the leading coefficient first and this often introduces fractions to the process. Solving by completing the square works well whenever the leading coefficient is 1 and the coefficient of the “x-term” is even. Isolate the squared term by subtracting 11. Here’s an example worked out for the equation. Use the sign when taking the square root of the constant term.
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