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: 60

Answer

$y=-4\pm\sqrt{2}i$

Work Step by Step

$y^{2}+8y+18=0$ Take the $18$ to the right side of the equation: $y^{2}+8y=-18$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this case, $b=8$ $y^{2}+8y+\Big(\dfrac{8}{2}\Big)^{2}=-18+\Big(\dfrac{8}{2}\Big)^{2}$ $y^{2}+8y+16=-2$ Factor the expression on the left side of the equation, which is a perfect square trinomial: $(y+4)^{2}=-2$ Take the square root of both sides of the equation: $\sqrt{(y+4)^{2}}=\sqrt{-2}$ $y+4=\pm\sqrt{2}i$ Solve for $y$" $y=-4\pm\sqrt{2}i$
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