Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.2 The Quadratic Formula - 11.2 Exercise Set - Page 713: 36


$x=\displaystyle \frac{3+\sqrt{19}i}{2}$ or $x=\displaystyle \frac{3-\sqrt{19}i}{2}$

Work Step by Step

$ x(x-1)=2x-7\qquad$... use the distributive property: $a(b+c)=ab+ac$. $ x^{2}-x=2x-7\qquad$...add $(-2x+7)$ to both sides. $ x^{2}-x-2x+7=2x-7-2x+7\qquad$...add like terms. $ x^{2}-3x+7=0\qquad$... solve with the Quadractic formula. $a=1,\ b=-3,\ c=7$ $ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $-3,\ a$ for $1$ and $c$ for $7$. $ x=\displaystyle \frac{-(-3)\pm\sqrt{(-3)^{2}-4\cdot(7)\cdot 1}}{2\cdot 1}\qquad$... simplify. $x=\displaystyle \frac{3\pm\sqrt{9-28}}{2}$ $ x=\displaystyle \frac{3\pm\sqrt{-19}}{2}\qquad$... write in terms of $i$. ($\sqrt{-1}=i$) $ x=\displaystyle \frac{3\pm\sqrt{19}i}{2}\qquad$... the symbol $\pm$ indicates two solutions. $x=\displaystyle \frac{3+\sqrt{19}i}{2}$ or $x=\displaystyle \frac{3-\sqrt{19}i}{2}$
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