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: 59

Answer

the solution set is\[\left\{ -2\pm \sqrt{11} \right\}\].

Work Step by Step

The given equation can be written as \[{{x}^{2}}+4x-7=0\]. Compare the given equation with the equation\[a{{x}^{2}}+bx+c=0\]. Here,\[a=1,\,\,b=4,\text{ and }c=-7\]. Now put these values in the quadratic formula: \[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] That is, \[\begin{align} & x=\frac{-4\pm \sqrt{{{\left( 4 \right)}^{2}}-4\times 1\times \left( -7 \right)}}{2\times 1} \\ & =\frac{-4\pm \sqrt{16+28}}{2} \\ & =\frac{-4\pm \sqrt{44}}{2} \\ & =-2\pm \sqrt{11} \end{align}\] Hence, the solution set is\[\left\{ -2\pm \sqrt{11} \right\}\].
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