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: 11


$x^2-\dfrac{4}{3}x+\dfrac{4}{9} \Rightarrow\left( x-\dfrac{2}{3} \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-\dfrac{4}{3}x ,$ the third term must be \begin{array}{l}\require{cancel}\left( \dfrac{-4/3}{2}\right)^2 \\\\= \left( \dfrac{-4}{6}\right)^2 \\\\= \left( \dfrac{-2}{3}\right)^2 \\\\= \dfrac{4}{9} .\end{array} Using $a^2\pm2ab+b^2=(a\pm b)^2$, then \begin{array}{l}\require{cancel} x^2-\dfrac{4}{3}x+\dfrac{4}{9} \Rightarrow\left( x-\dfrac{2}{3} \right)^2 .\end{array}
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