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: 64

Answer

$x=2\pm\dfrac{2}{3}i$

Work Step by Step

$9x^{2}-36x=-40$ Take out common factor $9$ from the left side of the equation: $9(x^{2}-4x)=-40$ Take the $9$ to divide the right side of the equation: $x^{2}-4x=-\dfrac{40}{9}$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this case, $b=-4$ $x^{2}-4x+\Big(\dfrac{-4}{2}\Big)^{2}=-\dfrac{40}{9}+\Big(\dfrac{-4}{2}\Big)^{2}$ $x^{2}-4x+4=-\dfrac{40}{9}+4$ $x^{2}-4x+4=-\dfrac{4}{9}$ Factor the expression on the left side of the equation, which is a perfect square trinomial: $(x-2)^{2}=-\dfrac{4}{9}$ Take the square root of both sides of the equation: $\sqrt{(x-2)^{2}}=\sqrt{-\dfrac{4}{9}}$ $x-2=\pm\dfrac{2}{3}i$ Solve for $x$: $x=2\pm\dfrac{2}{3}i$
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