Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Exercise Set 6.5 - Page 400: 67

Answer

the solution set is\[\left\{ \frac{1\pm \sqrt{57}}{2} \right\}\].

Work Step by Step

The given equation can be written as\[{{x}^{2}}-x-14=0\]. Compare the given equation with the equation\[a{{x}^{2}}+bx+c=0\]. Here,\[a=1,\,\,b=-1,\text{ and }c=-14\] Now put these values in the quadratic formula: \[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] That is, \[\begin{align} & x=\frac{1\pm \sqrt{{{\left( -1 \right)}^{2}}-4\times 1\times \left( -14 \right)}}{2\times 1} \\ & =\frac{1\pm \sqrt{1+56}}{2} \\ & =\frac{1\pm \sqrt{57}}{2} \end{align}\] Hence, the solution set is\[\left\{ \frac{1\pm \sqrt{57}}{2} \right\}\].
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.