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: 63

Answer

$x=1\pm\dfrac{\sqrt{2}}{2}i$

Work Step by Step

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