Introductory Algebra for College Students (7th Edition)

Published by Pearson

Chapter 6 - Section 6.6 - Solving Quadratic Equations by Factoring - Exercise Set - Page 473: 48

Answer

$x=-2$ or $x=-3$

Work Step by Step

$(x-3)(x+8)=-30\qquad$...apply the FOIL method. $x^{2}+8x-3x-24=-30\qquad$... add $30$ to both sides. $x^{2}+5x+6=0$ ... Searching for two factors of $ac=6$ whose sum is $b=5,$ we find$\qquad 2$ and $3.$ Rewrite the middle term and factor in pairs: $x^{2}+2x+3x+6=0$ $x(x+2)+3(x+2)=0$ $(x+2)(x+3)=0\qquad$...apply the principle of zero products. $x+2=0$ or $x+3=0$ $x=-2$ or $x=-3$ Type the equation into a graphing utility and see that the graph intercepts the x-axis at $-2$ and $-3$.

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