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: 55

Answer

{$-8-5\sqrt 2,-8+5\sqrt 2$}

Work Step by Step

Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain: Step 1: $2(x+8)^{2}-9=91$ Step 2: $2(x+8)^{2}=91+9$ Step 3: $2(x+8)^{2}=100$ Step 4: $(x+8)^{2}=50$ Step 5: $x+8=\pm \sqrt {50}$ Step 6: $x+8=\pm \sqrt {25\times2}$ Step 7: $x+8=\pm 5\sqrt {2}$ Step 8: $x+8=5\sqrt 2$ or $x+8=-5\sqrt 2$ Step 9: $x=-8+5\sqrt 2$ or $x=-8-5\sqrt 2$ The solution set is {$-8-5\sqrt 2,-8+5\sqrt 2$}.
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