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 - Connecting: The Concepts - Exercises - Page 712: 4


$x=-\displaystyle \frac{1}{2}+\frac{\sqrt{13}}{2}$ or $x=-\displaystyle \frac{1}{2}-\frac{\sqrt{13}}{2}$

Work Step by Step

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