Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 564: 27



Work Step by Step

$5n^2-3n-15=10$ Rewrite the equation as: $n^2-\frac{3}{5}n-3=2$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-\frac{3}{5}$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-\frac{3}{5})^2}{4}=\dfrac{9}{100}$ To complete the square, add $\dfrac{9}{100}$ on both sides. $n^2-\frac{3}{5}n-3+\dfrac{9}{100}=2+\dfrac{9}{100}$ $\implies (n-\dfrac{3}{10})^2=\dfrac{509}{100}$ $\implies (n-\dfrac{3}{10})=2.26$ and $\implies (n-\dfrac{3}{10})=-2.26$ or, $n=2.56,-1.96$
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