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 8.2 - The Quadratic Formula - Exercise Set - Page 608: 70



Work Step by Step

Set up the equation: Let $x$ be the number. Note that $x<0$. $2x^2 - (1+2x)=0$ $2x^2 - 1 - 2x =0$ $2x^2 -2x-1=0$ $x^2 -x-\frac{1}{2}=0$ $x^2 -x=\frac{1}{2}$ Compute for $x$ by completing the square. The coefficient of the $x$-term is $-1$; $(\frac{-1}{2})^2=\frac{1}{4}$ Add $\frac{1}{4}$ to both sides to complete the square. $x^2 -2x+\frac{1}{4}=\frac{1}{2}+\frac{1}{4}$ $x^2 -2x+\frac{1}{4}=\frac{3}{4}$ $(x-\frac{1}{2})^2=\frac{3}{4}$ $x-\frac{1}{2}=±\sqrt{\frac{3}{4}}$ $x=\frac{1}{2}±{\frac{\sqrt3}{2}}$ Since $x<0$, thus, $x={\frac{1-\sqrt{3}}{2}}$.
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