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: 30


$x=-\displaystyle \frac{3}{2}+\frac{\sqrt{37}}{2}$ or $x=-\displaystyle \frac{3}{2}-\frac{\sqrt{37}}{2}$

Work Step by Step

$ 5x(x-1)-7=4x(x-2)\qquad$... use the distributive property: $a(b+c)=ab+ac$. $ 5x^{2}-5x-7=4x^{2}-8x\qquad$...add $(-4x^{2}+8x)$ to both sides. $ 5x^{2}-5x-7-4x^{2}+8x=4x^{2}-8x-4x^{2}+8x\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{37}}{2}\qquad$... the symbol $\pm$ indicates two solutions. $x=-\displaystyle \frac{3}{2}+\frac{\sqrt{37}}{2}$ or $x=-\displaystyle \frac{3}{2}-\frac{\sqrt{37}}{2}$
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