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: 25

Answer

$x=-1\pm\frac{2\sqrt{15}}{5}$

Work Step by Step

We complete the square: $5x^{2}+10x-7=0$ $x^{2}+2x-\frac{7}{5}=0$ $x^{2}+2x=\frac{7}{5}$ $x^{2}+2x+1=\frac{7}{5}+1=\frac{12}{5}$ $(x+1)^{2}=\frac{12}{5}$ $x+1=\pm\sqrt{\frac{12}{5}}=\pm\sqrt{\frac{4*3*5}{5*5}}=\pm\frac{2\sqrt{15}}{5}$ $x=-1\pm\frac{2\sqrt{15}}{5}$
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