Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - 10.1 - Quadratic Equations - Problem Set 10.1: 42

Answer

{$-\frac{1}{2},-1$}

Work Step by Step

Using Property 10.1, which states that for any non-negative real number $a$, $(x+b)^{2}=a$ can be written as $x+b=\pm\sqrt a$, we obtain: Step 1: $(4x+3)^{2}=1$ Step 2: $4x+3=\pm \sqrt {1}$ Step 3: $4x+3=\pm 1$ Step 4: $4x+3=1$ or $4x+3=-1$ Step 5: $4x=1-3$ or $4x=-1-3$ Step 6: $4x=-2$ or $4x=-4$ Step 7: $x=-\frac{1}{2}$ or $x=-\frac{4}{4}=-1$ The solution set is {$-\frac{1}{2},-1$}.
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