Elementary Algebra

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

Chapter 10 - Quadratic Equations - 10.4 - Solving Quadratic Equations - Which Method? - Problem Set 10.4: 16

Answer

{$\frac{2 - \sqrt {10}}{3},\frac{2+\sqrt {10}}{3}$}

Work Step by Step

Step 1: Comparing $3x^{2}-4x-2=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=3$, $b=-4$ and $c=-2$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $x=\frac{-(-4) \pm \sqrt {(-4)^{2}-4(3)(-2)}}{2(3)}$ Step 4: $x=\frac{4 \pm \sqrt {16+24}}{6}$ Step 5: $x=\frac{4 \pm \sqrt {40}}{6}$ Step 6: $x=\frac{4 \pm \sqrt {4\times10}}{6}$ Step 7: $x=\frac{4 \pm (\sqrt {4}\times\sqrt {10})}{6}$ Step 8: $x=\frac{4 \pm (2\times \sqrt {10})}{6}$ Step 9: $x=\frac{2(2 \pm 1\sqrt {10})}{6}$ Step 10: $x=\frac{2 - \sqrt {10}}{3}$ or $x=\frac{2 + \sqrt {10}}{3}$ Step 11: Therefore, the solution set is {$\frac{2 - \sqrt {10}}{3},\frac{2+\sqrt {10}}{3}$}.
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