Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Appendix A - A.4 - Quadratic Equations - Exercises - Page 550: 31

Answer

$x=\frac{1}{3}~~$ or $~~x=\frac{1}{2}$

Work Step by Step

Let's consider a trinomial in this form: $~ax^2+bx+c$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = a\times c$ Then the next step is to rewrite the trinomial as follows: $~x^2+bx+c = ax^2+rx+sx+c$ We can rewrite the given equation: $6x^2 = 5x-1$ $6x^2 - 5x +1 = 0$ To factor the left side of this equation, we need to find two numbers $r$ and $s$ such that $r+s = -5~$ and $~r\times s = 6$. We can see that $(-2)+(-3) = -5~$ and $(-2)\times (-3) = 6$ We can solve the equation as follows: $6x^2 = 5x-1$ $6x^2 - 5x +1 = 0$ $6x^2 - 3x - 2x +1 = 0$ $(6x^2 - 3x)+(-2x +1) = 0$ $(3x)(2x - 1)+(-1)(2x - 1) = 0$ $(3x-1)~(2x-1) = 0$ $3x-1 = 0~~$ or $~~2x-1 = 0$ $x=\frac{1}{3}~~$ or $~~x=\frac{1}{2}$
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