Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Appendix A - A.4 - Quadratic Equations - Exercises - Page 550: 27

Answer

$x=5~$ or $~x=12$

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: $3x^2-51x+180=0$ $(3)~(x^2-17x+60)=0$ To factor the left side of the equation, we need to find two numbers $r$ and $s$ such that $r+s = -17$ and $r\times s = 60$. We can see that $(-5)+(-12) = -17~$ and $(-5)\times (-12) = 60$ We can solve the equation as follows: $3x^2-51x+180=0$ $(3)~(x^2-17x+60)=0$ $(3)~(x-5)(x-12)=0$ $x=5~$ or $~x=12$
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