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: 47


$x=-6$ or $x=3$

Work Step by Step

$(x-1)(x+4)=14\qquad$...apply the FOIL method. $ x^{2}+4x-x-4=14\qquad$... add $-14$ to both sides. $x^{2}+3x-18$ ... Searching for two factors of $ac=-18$ whose sum is $b=3,$ we find$\qquad 6$ and $-3.$ Rewrite the middle term and factor in pairs: $x^{2}+6x-3x-18=0$ $x(x+6)-3(x+6)=0$ $(x+6)(x-3)=0\qquad$...apply the principle of zero products. $x+6=0$ or $x-3=0$ $x=-6$ or $x=3$ Type the equation into a graphing utility and see that the graph intercepts the x-axis at $-6$ and $3$.
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