Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Exercise Set: 57

Answer

$x=\dfrac{1\pm\sqrt{47}i}{4}$

Work Step by Step

$2x^{2}-x+6=0$ Take the $6$ to the right side of the equation: $2x^{2}-x=-6$ Take out common factor $2$ from the left side of the equation: $2\Big(x^{2}-\dfrac{1}{2}x\Big)=-6$ Take the $2$ to divide the right side of the equation: $x^{2}-\dfrac{1}{2}x=\dfrac{-6}{2}$ $x^{2}-\dfrac{1}{2}x=-3$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. For this case, $b=-\dfrac{1}{2}$: $x^{2}-\dfrac{1}{2}x+\Big(\dfrac{-\frac{1}{2}}{2}\Big)^{2}=-3+\Big(\dfrac{-\frac{1}{2}}{2}\Big)^{2}$ $x^{2}-\dfrac{1}{2}x+\dfrac{1}{16}=-3+\dfrac{1}{16}$ $x^{2}-\dfrac{1}{2}x+\dfrac{1}{16}=-\dfrac{47}{16}$ Factor the left side of the equation, which is a perfect square trinomial: $\Big(x-\dfrac{1}{4}\Big)^{2}=-\dfrac{47}{16}$ Take the square root of both sides of the equation: $\sqrt{\Big(x-\dfrac{1}{4}\Big)^{2}}=\sqrt{-\dfrac{47}{16}}$ $x-\dfrac{1}{4}=\pm\dfrac{\sqrt{47}}{4}i$ Solve for $x$: $x=\dfrac{1\pm\sqrt{47}i}{4}$
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