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: 6


$x=\left\{ -7,4 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the solutions of the given equation, $ x^2+3x-28=0 ,$ use the Quadratic Formula. $\bf{\text{Solution Details:}}$ Using the form $ax^2+bx+c=0,$ the quadratic equation above has $a= 1 , b= 3 , c= -28 .$ Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, then \begin{array}{l}\require{cancel} x=\dfrac{-3\pm\sqrt{3^2-4(1)(-28)}}{2(1)} \\\\ x=\dfrac{-3\pm\sqrt{9+112}}{2} \\\\ x=\dfrac{-3\pm\sqrt{121}}{2} \\\\ x=\dfrac{-3\pm11}{2} .\end{array} The solutions are \begin{array}{l}\require{cancel} x=\dfrac{-3-11}{2} \\\\ x=\dfrac{-14}{2} \\\\ x=-7 \\\\\text{OR}\\\\ x=\dfrac{-3+11}{2} \\\\ x=\dfrac{8}{2} \\\\ x=4 .\end{array} Hence, $ x=\left\{ -7,4 \right\} .$
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