Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.2 - The Quadratic Formula - 8.2 Exercises: 5


$x=\left\{ 3,5 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the solutions of the given equation, $ x^2-8x+15=0 ,$ use the Quadratic Formula. $\bf{\text{Solution Details:}}$ Using the form $ax^2+bx+c=0,$ the quadratic equation above has $a= 1 , b= -8 , c= 15 .$ Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, then \begin{array}{l}\require{cancel} x=\dfrac{-(-8)\pm\sqrt{(-8)^2-4(1)(15)}}{2(1)} \\\\ x=\dfrac{8\pm\sqrt{64-60}}{2} \\\\ x=\dfrac{8\pm\sqrt{4}}{2} \\\\ x=\dfrac{8\pm2}{2} .\end{array} The solutions are \begin{array}{l}\require{cancel} x=\dfrac{8-2}{2} \\\\ x=\dfrac{6}{2} \\\\ x=3 \\\\\text{OR}\\\\ x=\dfrac{8+2}{2} \\\\ x=\dfrac{10}{2} \\\\ x=5 .\end{array} Hence, $ x=\left\{ 3,5 \right\} .$
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