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: 19


$t=3+i$ or $t=3-i$

Work Step by Step

$ t^{2}+10=6t\qquad$...add $-6t$ to both sides. $ t^{2}-6t+10=0\qquad$... solve with the Quadractic formula. $a=1,\ b=-6,\ c=10$ $ t=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $-6,\ a$ for $1$ and $c$ for $10$. $ t=\displaystyle \frac{-(-6)\pm\sqrt{(-6)^{2}-4\cdot(10)\cdot 1}}{2\cdot 1}\qquad$... simplify. $t=\displaystyle \frac{6\pm\sqrt{36-40}}{2}$ $ t=\displaystyle \frac{6\pm\sqrt{-4}}{2}\qquad$... write in terms of $i$. ($\sqrt{-1}=i$) $t=\displaystyle \frac{6\pm 2i}{2}$ $ t=3\pm i\qquad$... the symbol $\pm$ indicates two solutions. $t=3+i$ or $t=3-i$
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