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: 14


$x=-\displaystyle \frac{5}{2}+\frac{\sqrt{13}}{2}$ or $x=-\displaystyle \frac{5}{2}-\frac{\sqrt{13}}{2}$

Work Step by Step

$ x^{2}+5x+3=0\qquad$... solve with the Quadractic formula. $a=1,\ b=5,\ c=3$ $ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $5,\ a$ for $1$ and $c$ for $3$. $ x=\displaystyle \frac{-5\pm\sqrt{(5)^{2}-4\cdot(3)\cdot 1}}{2\cdot 1}\qquad$... simplify. $x=\displaystyle \frac{-5\pm\sqrt{25-12}}{2}$ $ x=\displaystyle \frac{-5\pm\sqrt{13}}{2}\qquad$... the symbol $\pm$ indicates two solutions. $x=-\displaystyle \frac{5}{2}+\frac{\sqrt{13}}{2}$ or $x=-\displaystyle \frac{5}{2}-\frac{\sqrt{13}}{2}$
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