Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Appendix A - A.4 - Quadratic Equations - Exercises - Page 556: 30

Answer

$x=-7~~$ or $~~x=2$

Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$ Then we can factor the trinomial as follows: $~x^2+bx+c = (x+r)~(x+s)$ We can use the GCF to factor the left side of the given equation: $8x^2+40x-112=0$ $(8)~(x^2+5x-14)=0$ To factor the left side of the equation, we need to find two numbers $r$ and $s$ such that $r+s = 5$ and $r\times s = -14$. We can see that $(7)+(-2) = 5~$ and $(7)\times (-2) = -14$ We can solve the equation as follows: $8x^2+40x-112=0$ $(8)~(x^2+5x-14)=0$ $(8)~(x+7)(x-2)=0$ $x=-7~~$ or $~~x=2$
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