Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 593: 47


{$-\dfrac{1}{2} - \dfrac{\sqrt{5}}{2},-\dfrac{1}{2} + \dfrac{\sqrt{5}}{2}$}

Work Step by Step

Given: $x^2+x-1=0$ This can be re-written as: $x^2+x=-1$ We will have to add both sides $(\dfrac{1}{2})^2$ to complete the square. Thus, $x^2+x+(\dfrac{1}{2})^2=-1+(\dfrac{1}{2})^2$ or, $(x+\dfrac{1}{2})^2=\dfrac{5}{4}$ or, $(x+\dfrac{1}{2})=\pm\sqrt{\dfrac{5}{4}}$ or, $x=-\dfrac{1}{2} \pm \dfrac{\sqrt{5}}{2}$ Hence, our desired solution set is {$-\dfrac{1}{2} - \dfrac{\sqrt{5}}{2},-\dfrac{1}{2} + \dfrac{\sqrt{5}}{2}$}
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