Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 8 - Section 8.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 485: 67

Answer

$x=\left\{ -5-i\sqrt{3},-5+i\sqrt{3} \right\}$

Work Step by Step

Using the completing the square method, the solutions of the given quadratic equation, $ x^2+10x+28=0 ,$ is \begin{array}{l}\require{cancel} x^2+10x=-28 \\\\ x^2+10x+\left( \dfrac{10}{2} \right)^2=-28+\left( \dfrac{10}{2} \right)^2 \\\\ x^2+10x+25=-28+25 \\\\ (x+5)^2=-3 \\\\ x+5=\pm\sqrt{-3} \\\\ x+5=\pm i\sqrt{3} \\\\ x=-5\pm i\sqrt{3} .\end{array} Hence, $ x=\left\{ -5-i\sqrt{3},-5+i\sqrt{3} \right\} .$
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