Intermediate Algebra (6th Edition)

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

Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set: 22

Answer

The solutions are $m=2$ and $m=5$.

Work Step by Step

Let $u=m-6$ Rewrite the given equation using the variable $u$ to obtain: $u^2+5u+4=0$ Factor the trinomial to obtain: $(u+4)(u+1)=0$ Use the Zero-Factor Property by equating each unique factor to zero. then solve: $u+4 = 0 \text{ or } u+1=0 \\u=-4 \text{ or } u=-1$ Since $u=m-6$, then \begin{array}{ccc} &u= -4 &\text{or} &u=-1 \\&m-6=-4 &\text{or} &m-6=-1 \\&m=-4+6 &\text{or} &m=-1+6 \\&m=2 &\text{or} &m=5 \end{array} Thus, the solutions are $m=2$ and $m=5$.
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