Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 775: 21


$m=1$ and $m=\dfrac{5}{2}$

Work Step by Step

$(m+2)(2m-6)=5(m-1)-12$ Evaluate the products present on both sides of the equation: $2m^{2}-2m-12=5m-5-12$ Take all terms to the left side of the equation: $2m^{2}-2m-12-5m+5+12=0$ Simplify the equation by combining like terms: $2m^{2}-7m+5=0$ Use the quadratic formula to solve the resulting equation. The formula is $m=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=2$, $b=-7$ and $c=5$ Substitute: $m=\dfrac{-(-7)\pm\sqrt{(-7)^{2}-4(2)(5)}}{2(2)}=\dfrac{7\pm\sqrt{49-40}}{4}=...$ $...=\dfrac{7\pm\sqrt{9}}{4}=\dfrac{7\pm3}{4}$ Our two solutions are: $m=\dfrac{7-3}{4}=1$ $m=\dfrac{7+3}{4}=\dfrac{5}{2}$
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