using square roots to solve quadratic equations

Therefore, it is reasonable to transform the original equation intoįrom the last equation, which is absolutely equivalent to the original one, using the operation of the square root, we derive two linear equations: So, let's transform our equation to this form.Įxpression #x^2+x# is not a square of anything, but #x^2+x+1/4# is a square of #x+1/2# because If we could transform it to something like #y^2=b# then the square root of both sides would deliver a solution. Here is the idea.Īssume, for example, the same equation as analyzed in the previous answer: However, with certain transformation of a given equation into a different but equivalent form it is possible. If the question is about using the square root directly against the equation, the answer is definitely NO. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License.

We recommend using aĪuthors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis 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. The sides of the deck are 8, 15, and 17 feet. Since x is a side of the triangle, x = −8 x = −8 does not Since this is a right triangle we can use the We are looking for the lengths of the sides Use the formula for the area of a rectangle. The area of the rectangular garden is 15 square feet. Restate the important information in a sentence. In problems involving geometric figures, a sketch can help you visualize the situation. Both pairs of consecutive integers are solutions. If the first integer is n = 11 If the first integer is n = −12 then the next integer is n + 1 then the next integer is n + 1 11 + 1 −12 + 1 12 −11 If the first integer is n = 11 If the first integer is n = −12 then the next integer is n + 1 then the next integer is n + 1 11 + 1 −12 + 1 12 −11 So there are two sets of consecutive integers that will work. There are two values for n n that are solutions to this problem. The first integer times the next integer is 132. The product of the two consecutive integers is 132. Let n = the first integer n + 1 = the next consecutive integer Let n = the first integer n + 1 = the next consecutive integer We are looking for two consecutive integers.

Using square roots to solve quadratic equations