Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.2 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 638: 8


$x^2-x+\dfrac{1}{4} \Rightarrow\left( x-\dfrac{1}{2} \right)^2 $

Work Step by Step

The third term of a perfect square trinomial is equal to the square of half the coefficient of the middle term. Hence, to complete the square of the given expression $ x^2-x ,$ the third term must be \begin{array}{l}\require{cancel}\left( \dfrac{-1}{2}\right)^2 \\\\= \dfrac{1}{4} .\end{array} Using $a^2\pm2ab+b^2=(a\pm b)^2$, then \begin{array}{l}\require{cancel} x^2-x+\dfrac{1}{4} \Rightarrow\left( x-\dfrac{1}{2} \right)^2 .\end{array}
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