What did you do to become confident of your ability to do these things? Be specific. Reflect on the study skills you used so that you can continue to use them. Congratulations! You have achieved the objectives in this section. Ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.Ĭhoose how would you respond to the statement “I can solve quadratic equations of the form a times the square of x minus h equals k using the Square Root Property.” “Confidently,” “with some help,” or “No, I don’t get it.” Since these equations are all of the form x 2 = k, the square root definition tells us the solutions are the two square roots of k. If n 2 = m, then n is a square root of m. We earlier defined the square root of a number in this way: So, every positive number has two square roots-one positive and one negative. Therefore, both 13 and −13 are square roots of 169. Previously we learned that since 169 is the square of 13, we can also say that 13 is a square root of 169. īut what happens when we have an equation like x 2 = 7? Since 7 is not a perfect square, we cannot solve the equation by factoring. In each case, we would get two solutions, x = 4, x = −4 x = 4, x = −4 and x = 5, x = −5. We can easily use factoring to find the solutions of similar equations, like x 2 = 16 and x 2 = 25, because 16 and 25 are perfect squares. Let’s review how we used factoring to solve the quadratic equation x 2 = 9. We have already solved some quadratic equations by factoring. Solve Quadratic Equations of the form a x 2 = k a x 2 = k using the Square Root Property 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.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |