Elementary Algebra

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

Chapter 10 - Quadratic Equations - 10.3 - Quadratic Formula - Problem Set 10.3: 42

Answer

{$\frac{-1-\sqrt {21}}{10},\frac{-1+\sqrt {21}}{10}$}

Work Step by Step

Step 1: Comparing $5x^{2}+x-1=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=5$, $b=1$ and $c=-1$ 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: $x=\frac{-(1) \pm \sqrt {(1)^{2}-4(5)(-1)}}{2(5)}$ Step 4: $x=\frac{-1 \pm \sqrt {1+20}}{10}$ Step 5: $x=\frac{-1 \pm \sqrt {21}}{10}$ Step 6: $x=\frac{-1-\sqrt {21}}{10}$ or $x=\frac{-1+\sqrt {21}}{10}$ Step 7: Therefore, the solution set is {$\frac{-1-\sqrt {21}}{10},\frac{-1+\sqrt {21}}{10}$}.
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