Intermediate Algebra (6th Edition)

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

Chapter 9 - Section 9.3 - Exponential Functions - Exercise Set - Page 560: 55


$x=2$ and $x=3$

Work Step by Step

We are given that $x^{2}+6=5x$. We can first subtract 5x from both sides of the equation to get all terms on one side. $x^{2}-5x+6=0$ We know that 2 and 3 are factors of six and the sum of -2 and -3 is equal to $-2+(-3)=-5$ (which is the coefficient attached to the middle term). Therefore, we can factor the existing polynomial into $(x-2)(x-3)=0$ Set both terms in parentheses equal to 0. $x-2=0$ Add 2 to both sides. $x=2$ $x-3=0$ Add 3 to both sides. $x=3$
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