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: 39

Answer

$\frac{ 3 \pm \sqrt3 }{2}$

Work Step by Step

We first get rid of all of the fractions and get everything on one side of the equation: $2x^2 -6x = -3 \\ 2x^2 -6x + 3 = 0 $ We apply the quadratic formula: $ x = \frac{ -b \pm \sqrt{b^2 -4ac}}{2a} \\ x = \frac{6 \pm \sqrt{(-6)^2 -4(2)(3)}}{2(2)} \ \\ x = \frac{6 \pm \sqrt{(12)}}{4} \\ x = \frac{ 3 \pm \sqrt3 }{2}$
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