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: 22

Answer

$x=\displaystyle \frac{5}{2}\pm\frac{\sqrt{21}}{2}$

Work Step by Step

We complete the square: $x^{2}-5x+1=0$ $x^{2}-5x=-1$ $x^{2}-5x+\frac{25}{4}=-1+\frac{25}{4}=-\frac{4}{4}+\frac{25}{4}=\frac{21}{4}$ $(x-\frac{5}{2})^{2}=\frac{21}{4}$ $x-\frac{5}{2}=\pm\sqrt{\frac{21}{4}}=\pm\frac{\sqrt{21}}{2}$ $x=\displaystyle \frac{5}{2}\pm\frac{\sqrt{21}}{2}$
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