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: 43



Work Step by Step

Given: $x^2+3x-1=0$ This can be re-written as: $x^2+3x=1$ We will have to add both sides $(\dfrac{3}{2})^2$ to complete the square. Thus, $x^2+3x+(\dfrac{3}{2})^2=1+(\dfrac{3}{2})^2$ or, $(x+\dfrac{3}{2})^2=\dfrac{13}{4}$ or, $(x+\dfrac{3}{2})=\pm\sqrt{\dfrac{13}{4}}$ Hence, our desired solution set is {$-\dfrac{3}{2}+\dfrac{\sqrt{13}}{2},-\dfrac{3}{2}-\dfrac{\sqrt{13}}{2}$}
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