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: 73



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: $$ 2x^2-3x=1\\ x^2-\frac{3x}{2}=\frac{1}{2}\\ x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{1}{2}+\left(-\frac{3}{4}\right)^2\\ \left(x-\frac{3}{4}\right)^2=\frac{17}{16}\\ x=\frac{\sqrt{17}+3}{4},\:x=\frac{-\sqrt{17}+3}{4}$$
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