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Simple Quadratic Equations

Simple Quadratic Equations. ax ˆ2 + bx + c = 0. By Marian Haara. Before you can solve a quadratic equation, you have to understand a little bit about them. Quadratic equations are typically in the form: axˆ2 + bx + c = 0.

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Simple Quadratic Equations

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  1. Simple Quadratic Equations axˆ2 + bx + c = 0 By Marian Haara

  2. Before you can solve a quadratic equation, you have to understand a little bit about them. Quadratic equations are typically in the form: axˆ2 + bx + c = 0

  3. The letters 'a', 'b', and 'c' are just numbers that will be used later on. 'a' cannot be zero, though. The easiest way to solve a quadratic equation is by factoring. This is the first way we are going to solve them.

  4. The simplest quadratic equation is already in factored form. Factored form looks like this: (x + 7) (x - 3) = 0 To solve the equation from here, set each of the x's equal to zero. Like this: x + 7 = 0 or x - 3 = 0

  5. That step leaves you with two equations that are very easy to solve. Now all you have to do is subtract three from the first equation and add two in the second equation. This step leaves you with the answers and looks like this: x = -7 or x = 3

  6. Solving factored quadratic equations is done in three easy steps. Put these steps together and it looks like this: (x + 7) (x - 3)= 0 x + 7 = 0 or x - 3 = 0 x = - 3 or x = 3

  7. The non-factored quadratic equations are in the form: axˆ2 + bx + c = 0 These equations only require one more step than the factored equations we just did. Let's try this one: xˆ2 + 3x - 10 = 0

  8. The first thing you need to do is factor the equation. In order to factor the equation and make it look like the problem we just did, you have to consider the factors of eight. The possibilities include one & ten and two & five.

  9. The only possible combination is the one that when added or subtracted gives a three for the answer. The factorization for this equation looks like this. (x + 5) (x - 2) = 0

  10. If you were to multiply the factors out using FOIL, you would obtain the original equation. Now you can use the same steps as before to finish solving this equation. To solve the equation from here, set each of the x's equal to zero. Like this: (x + 5) = 0 or (x - 2) = 0

  11. This step leaves you with two equations that are very easy to solve. Now all you have to do is subtract four from the first equation and add two in the second equation. This step gives you the answers and looks like this: x = -5 or x = 2

  12. Solving non-factored quadratic equations only takes one more step than the factored ones. Put these steps together and it looks like this: xˆ2 + 3x - 10 = 0 (x + 5) (x - 2) = 0 (x + 5) = 0 or (x - 2) = 0 x = -5 or x = 2

  13. Now you are ready to work on the practice problems. Click the link below to practice your quadratic skills, and then check your answers. Practice Quadratic Equations Practice Quadratic Equations Answers Back to Main Page

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