Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.1 Quadratic Equations - 11.1 Exercise Set - Page 707: 71



Work Step by Step

To find the x-intercepts, we set the equation equal to zero and then complete the square. Doing this, we find: $$ x^2+\frac{x}{2}=\frac{3}{4}\\ x^2+\frac{x}{2}+\left(\frac{1}{4}\right)^2=\frac{3}{4}+\left(\frac{1}{4}\right)^2\\ \left(x+\frac{1}{4}\right)^2=\frac{13}{16}\\ x=\frac{\sqrt{13}-1}{4},\:x=\frac{-\sqrt{13}-1}{4}$$
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