Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 8 - Sections 8.1-8.3 - Integrated Review - Summary on Solving Quadratic Equations: 21

Answer

$x=2\pm\sqrt{6}$

Work Step by Step

Using the Distributive Property and the properties of equality, the given quadratic equation, $ x(x-2)=5 ,$ is equivalent to \begin{array}{l}\require{cancel} x^2-2x=5 \\\\ x^2-2x-5=0 .\end{array} Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are \begin{array}{l}\require{cancel} x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(-5)}}{2(1)} \\\\ x=\dfrac{4\pm\sqrt{4+20}}{2} \\\\ x=\dfrac{4\pm\sqrt{24}}{2} \\\\ x=\dfrac{4\pm\sqrt{4\cdot6}}{2} \\\\ x=\dfrac{4\pm\sqrt{(2)^2\cdot6}}{2} \\\\ x=\dfrac{4\pm2\sqrt{6}}{2} \\\\ x=\dfrac{2(2\pm\sqrt{6})}{2} \\\\ x=\dfrac{\cancel{2}(2\pm\sqrt{6})}{\cancel{2}} \\\\ x=2\pm\sqrt{6} .\end{array}
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