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: 1

Answer

$x^2+10x+25 \Rightarrow (x+5)^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+10x ,$ the third term must be \begin{array}{l}\require{cancel}\left( \dfrac{10}{2} \right)^2\\\\=\left( 5 \right)^2\\\\= 25 .\end{array} Hence, $ x^2+10x+25 \Rightarrow (x+5)^2 .$
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