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: 54

Answer

{$0,\frac{5}{2}$}

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: $3(4x-5)^{2}-50=25$ Step 2: $3(4x-5)^{2}=25+50$ Step 3: $3(4x-5)^{2}=75$ Step 4: $(4x-5)^{2}=25$ Step 5: $4x-5=\pm \sqrt {25}$ Step 6: $4x-5=\pm 5$ Step 7: $4x-5=5$ or $4x-5=-5$ Step 8: $4x=5+5$ or $4x=-5+5$ Step 9: $4x=10$ or $4x=0$ Step 10: $x=\frac{10}{4}$ or $x=\frac{0}{4}$ Step 11: $x=\frac{5}{2}$ or $x=0$ The solution set is {$0,\frac{5}{2}$}.
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