Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set: 49

Answer

$x=\left\{ 4,6 \right\}$

Work Step by Step

The factored form of the given expression, $ \dfrac{x^2}{4}-\dfrac{5}{2}x+6=0 $, is \begin{array}{} 4\left( \dfrac{x^2}{4}-\dfrac{5}{2}x+6 \right)=(0)4 \\\\ 1(x^2)-2(5x)+4(6)=0 \\\\ x^2-10x+24=0 \\\\ (x-6)(x-4)=0 .\end{array} Equating each factor to zero, then \begin{array}{l} x-6=0 \\ x=0+6 \\ x=6 ,\text{ OR}\\\\ x-4=0 \\ x=0+4 \\ x=4 \end{array} Hence, $ x=\left\{ 4,6 \right\} $.
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