College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.4 - Solving Quadratic Equations - 1.4 Exercises: 27

Answer

$x=-\frac{7}{4}\pm\frac{\sqrt{17}}{4}$

Work Step by Step

We complete the square: $2x^{2}+7x+4=0$ $x^{2}+\frac{7}{2}x+2=0$ $x^{2}+\frac{7}{2}x=-2$ $x^{2}+\frac{7}{2}x+\frac{49}{16}=-2+\frac{49}{16}=\frac{17}{16}$ $(x+\frac{7}{4})^{2}=\frac{17}{16}$ $x+\displaystyle \frac{7}{4}=\pm\sqrt{\frac{17}{16}}=\pm\frac{\sqrt{17}}{4}$ $x=-\frac{7}{4}\pm\frac{\sqrt{17}}{4}$
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