Introductory Algebra for College Students (7th Edition)

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

Chapter 6 - Section 6.6 - Solving Quadratic Equations by Factoring - Exercise Set - Page 473: 49


$x=-1$ or $x=-6$

Work Step by Step

$(x+1)(2x+5)=-1\qquad$...apply the FOIL method. $ x^{2}+5x+2x+5=-1\qquad$... add $1$ to both sides. $x^{2}+7x+6=0$ ... Searching for two factors of $ac=6$ whose sum is $b=7,$ we find$\qquad 1$ and $6.$ Rewrite the middle term and factor in pairs: $x^{2}+x+6x+6=0$ $x(x+1)+6(x+1)=0$ $(x+1)(x+6)=0\qquad$...apply the principle of zero products. $x+1=0$ or $x+6=0$ $x=-1$ or $x=-6$ Type the equation into a graphing utility and see that the graph intercepts the x-axis at $-1$ and $-6$.
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