Algebra: A Combined Approach (4th Edition)

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

Chapter 6 - Section 6.6 - Solving Quadratic Equations by Factoring - Exercise Set: 49

Answer

The solutions are $\frac{6}{5}$ and $\frac{-5}{6}$.

Work Step by Step

30$x^{2}$-11x=30 30$x^{2}$-11x-30=30-30 30$x^{2}$-11x-30=0 30$x^{2}$+25x-36x-30=0 5x(6x+5)-6(6x+5)=0 (5x-6)(6x+5)=0 (5x-6) =0 or (6x+5)=0 5x-6+6=0+6 or 6x+5-5=0-5 5x=6 or 6x=-5 x=$\frac{6}{5}$ or x=$\frac{-5}{6}$ The solutions are $\frac{6}{5}$ and $\frac{-5}{6}$. Check Let x= $\frac{6}{5}$ 30$x^{2}$-11x=30 30$(6/5)^{2}$-11$\frac{6}{5}$=30 30*36/25-$\frac{66}{5}$=30 6*36/5-$\frac{66}{5}$=30 216/5-$\frac{66}{5}$=30 150/5=30 30=30 Let x= $\frac{-5}{6}$ 30$x^{2}$-11x=30 30$(-5/6)^{2}$-11$\frac{-5}{6}$=30 30*25/36+$\frac{55}{6}$=30 5*25/6+$\frac{55}{6}$=30 125/6+$\frac{55}{6}$=30 180/6=30 30=30
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