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: 12


$t=-2+\sqrt{5}$ or $t=-2-\sqrt{5}$

Work Step by Step

$ t^{2}+4t=1\qquad$...square half the coefficient of $x$ and add it to both sides to complete the square $(\displaystyle \frac{4}{2})=2,\ (2)^{2}=4\qquad$...add $4$ to both sides. $ t^{2}+4t+4=5\\qquad$...write $t^{2}+4t+4$ as a binomial squared. $(t+2)^{2}=5\qquad$...use the principle of square roots: For any real number $k$ and any algebraic expression $X$ : $\text{If }X^{2}=k,\text{ then }X=\sqrt{k}\text{ or }X=-\sqrt{k}$ $ t+2=\pm\sqrt{5}\qquad$...add $-2$ to both sides. $ t=-2\pm\sqrt{5}\qquad$... the symbol $\pm$ indicates two solutions. $t=-2+\sqrt{5}$ or $t=-2-\sqrt{5}$
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