Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Section 8.2 - The Quadratic Formula - Exercise Set - Page 609: 74


$x=-\sqrt{3}+2i$ or $x=-\sqrt{3}-2i$

Work Step by Step

$\sqrt{3}x^2+6x+7\sqrt{3}=0$ Solve by using the quadratic formula: ^$x=\frac{−b±\sqrt{b^2−4ac}}{2a}$ $a=\sqrt{3}$, $b=6$, $c=7\sqrt{3}$ $x=\frac{−6±\sqrt{(6)^2−(4⋅\sqrt{3}⋅7\sqrt{3})}}{2⋅\sqrt{3}}$ $x=\frac{−6±\sqrt{36−(84)}}{2\sqrt{3}}$ $x=\frac{−6±\sqrt{-48}}{2\sqrt{3}}$ $x=\frac{−6±4\sqrt{-3}⋅\sqrt{-1}}{2\sqrt{3}}$ $x=\frac{−6±4\sqrt{3}i}{2\sqrt{3}}$ $x=\frac{−6+4\sqrt{3}i}{2\sqrt{3}}$ or $x=\frac{−6-4\sqrt{3}i}{2\sqrt{3}}$ $x=\frac{2(−3+2\sqrt{3}i)}{2\sqrt{3}}$ or $x=\frac{2(−3-2\sqrt{3}i)}{2\sqrt{3}}$ $x=\frac{−3+2\sqrt{3}i}{\sqrt{3}}$ or $x=\frac{−3-2\sqrt{3}i}{\sqrt{3}}$ $x=\frac{\sqrt{3}(−\sqrt{3}+2i)}{\sqrt{3}}$ or $x=\frac{\sqrt{3}(−\sqrt{3}-2i)}{\sqrt{3}}$ $x=-\sqrt{3}+2i$ or $x=-\sqrt{3}-2i$
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