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Then you must include on every physical page the following attribution: Solve Quadratic Equations Using the Quadratic Formula Now for the most important result you will see in this class, the quadratic formula which gives you a solution to a quadratic equation. If you are redistributing all or part of this book in a print format, Sometimes, we will need to do some algebra to get the equation into standard form before we can use the Quadratic Formula. Remember, to use the Quadratic Formula, the equation must be written in standard form, ax2 + bx + c 0. Want to cite, share, or modify this book? This book uses the Solve by using the Quadratic Formula: 5b2 + 2b + 4 0 5 b 2 + 2 b + 4 0. When a quadratic equation is written in standard form so that the values a, b, and c are readily determined, the equation can be solved using the quadratic formula. This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. The solutions to a quadratic equation of the form ax2 + bx + c 0, a 0 are given by the formula: x b ± b2 4ac 2a. A quadratic equation is a polynomial equation in a single variable where the highest exponent of the variable is 2. Rule for Using the Quadratic Formula The equation. x equals the opposite of b, plus or minus the square root of b squared minus 4 a c, all divided by 2 a. You can read this formula as: Where a 0 and b 2 4 a c 0. We start with the standard form of a quadratic equation and solve it for x by completing the square. Quadratic formula is used to solve any kind of quadratic equation. Now we will go through the steps of completing the square using the general form of a quadratic equation to solve a quadratic equation for x. We have already seen how to solve a formula for a specific variable ‘in general’, so that we would do the algebraic steps only once, and then use the new formula to find the value of the specific variable. In this section we will derive and use a formula to find the solution of a quadratic equation.
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The ± sign means there are two values, one with. Solution: Step 1: From the equation: a 4, b 26 and c 12. Example: Find the values of x for the equation: 4x 2 + 26x + 12 0. Mathematicians look for patterns when they do things over and over in order to make their work easier. Given the quadratic equation ax 2 + bx + c, we can find the values of x by using the Quadratic Formula: Let us consider an example. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes’. When we solved quadratic equations in the last section by completing the square, we took the same steps every time. Solve Quadratic Equations Using the Quadratic Formula If you missed this problem, review Example 8.76.