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: 11

Answer

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

Work Step by Step

Step 1: Comparing $y^{2}+4y+2=0$ to the standard form of a quadratic equation $ay^{2}+by+c=0$, we obtain: $a=1$, $b=4$ 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: $x=\frac{-(4) \pm \sqrt {(4)^{2}-4(1)(2)}}{2(1)}$ Step 4: $x=\frac{-4\pm \sqrt {16-8}}{2}$ Step 5: $x=\frac{-4 \pm \sqrt {8}}{2}$ Step 6: $x=\frac{-4 \pm \sqrt {4\times2}}{2}$ Step 7: $x=\frac{-4 \pm \sqrt {2^{2}\times2}}{2}$ Step 8: $x=\frac{-4 \pm 2\sqrt {2}}{2}$ Step 9: $x=-2\pm\sqrt 2$ Step 10: $x=-2+\sqrt 2$ or $x=-2-\sqrt 2$ Step 11: Therefore, the solution set is {$-2-\sqrt 2,-2+\sqrt 2$}.
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