In this section we will derive and use a formula to find the solution of a quadratic equation. Mathematicians look for patterns when they do things over and over in order to make their work easier. 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 Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, MaryAnne Anthony-Smith Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the 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. We can use the formula s = A s = A to find the length of a side of a square for a given area. A = s A = s 2 Take the square root of both sides. What if we want to find the length of a side for a given area? Then we need to solve the equation for s.Ī = s 2 Take the square root of both sides. The formula A = s 2 A = s 2 gives us the area of a square if we know the length of a side. If we let s be the length of a side of a square, the area of the square is s 2 s 2. A square is a rectangle in which the length and width are equal. W to find the area of a rectangle with length L and width W.Answer the question with a complete sentence. Check the answer in the problem and make sure it makes sense. Solve the equation using good algebra techniques. Translate into an equation by writing the appropriate formula or model for the situation. Name what we are looking for by choosing a variable to represent it. When appropriate, draw a figure and label it with the given information. Read the problem and make sure all the words and ideas are understood. (Both solutions should work.) The solutions are q = 6 and q = 2. q − 6 = 0 q − 2 = 0 q = 6 q = 2 The checks are left to you. 0 = 9 ( q 2 − 8 q + 12 ) 0 = 9 ( q − 6 ) ( q − 2 ) Use the zero product property. 0 = 9 q 2 − 72 q + 108 Factor the right side. 36 q − 72 = 9 q 2 − 36 q + 36 It is a quadratic equation, so get zero on one side. ( 6 q − 2 ) 2 = ( 3 q − 6 ) 2 Simplify, then solve the new equation. q − 2 + 6 q − 2 + 9 = 4 q + 1 There is still a radical in the equation. q − 2 + 3 = 4 q + 1 The radical on the right side is isolated. Q − 2 + 3 = 4 q + 1 The radical on the right side is isolated.
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