Intermediate Algebra (6th Edition)

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

Chapter 8 - Section 8.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 485: 69

Answer

$x=\left\{ -4,1 \right\}$

Work Step by Step

Using the completing the square method, the solutions of the given quadratic equation, $ z^2+3z-4=0 ,$ is \begin{array}{l}\require{cancel} z^2+3z=4 \\\\ z^2+3z+\left( \dfrac{3}{2}\right)^2=4+\left( \dfrac{3}{2}\right)^2 \\\\ z^2+3z+\dfrac{9}{4}=4+\dfrac{9}{4} \\\\ \left( z+\dfrac{3}{2}\right)^2=\dfrac{16}{4}+\dfrac{9}{4} \\\\ \left( z+\dfrac{3}{2}\right)^2=\dfrac{25}{4} \\\\ z+\dfrac{3}{2}=\pm\sqrt{\dfrac{25}{4}} \\\\ z+\dfrac{3}{2}=\pm\dfrac{5}{2} \\\\ z=-\dfrac{3}{2}\pm\dfrac{5}{2} \\\\ z=\dfrac{-3\pm5}{2} .\end{array} Hence, $ x=\left\{ -4,1 \right\} .$
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