Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Review - Page 828: 5

Answer

$z = (-3+\sqrt 5)/2$

Work Step by Step

$z^2+3z+1=0$ $z^2+3z+1+(3/2)^2=(3/2)^2$ $z^2+3z+1+9/4=9/4/$ $z^2+3z+9/4 +1=9/4$ $(z+3/2)^2+1=9/4$ $(z+3/2)^2+1-1=9/4-1$ $(z+3/2)^2 = 5/4$ $\sqrt{(z+3/2)^2} =\sqrt{5/4}$ $z+3/2 = \sqrt {5/4}$ $z+3/2-3/2 = \sqrt {5/4}-3/2$ $z= -3/2 +\sqrt {5/4}$ $z= -3/2 +\sqrt 5/\sqrt 4$ $z= -3/2 +\sqrt 5/2$ $z = (-3+\sqrt 5)/2$
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