Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Test - Page 832: 12

Answer

$a =\frac{2±i\sqrt {6}}{2}$

Work Step by Step

$2a^2+5=4a$ $2a^2+5-4a=4a-4a$ $2a^2-4a+5=0$ $(2a^2-4a+5)/2=0/2$ $a^2-2a+5/2=0$ $a^2-2a+5/2+(-2/2)^2=0+(-2/2)^2$ $a^2-2a+5/2+(-1)^2=0+(-1)^2$ $a^2-2a+5/2+1=0+1$ $a^2-2a+5/2+1-5/2=0+1-5/2$ $a^2-2a+1=-3/2$ $(a-1)^2=-3/2$ $\sqrt {(a-1)^2} =\sqrt {-3/2}$ $(a-1) =\sqrt {-3*2/2*2}$ $(a-1) =\frac{\sqrt {-6}}{\sqrt 4}$ $(a-1) =\frac{\sqrt {-6}}{2}$ $(a-1) =\frac{±i\sqrt {6}}{2}$ $a-1+1 =1+\frac{±i\sqrt {6}}{2}$ $a-1+1 =\frac {2}{2}+\frac{±i\sqrt {6}}{2}$ $a =\frac{2±i\sqrt {6}}{2}$
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