Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set: 27

Answer

$x=\dfrac{3}{8}\pm\dfrac{\sqrt{87}}{8}i$

Work Step by Step

$6=-4x^{2}+3x$ Rewrite the equation by taking all terms to the left side of the equation: $4x^{2}-3x+6=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=4$, $b=-3$ and $c=6$ Substitute: $x=\dfrac{-(-3)\pm\sqrt{(-3)^{2}-4(4)(6)}}{2(4)}=\dfrac{3\pm\sqrt{9-96}}{8}=...$ $...=\dfrac{3\pm\sqrt{-87}}{8}=\dfrac{3\pm\sqrt{87}i}{8}=\dfrac{3}{8}\pm\dfrac{\sqrt{87}}{8}i$
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