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: 53

Answer

$y=-1\pm i$

Work Step by Step

$y^{2}+2y+2=0$ Take the $2$ to the right side of the equation: $y^{2}+2y=-2$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. For this particular case, $b=2$ $y^{2}+2y+\Big(\dfrac{2}{2}\Big)^{2}=-2+\Big(\dfrac{2}{2}\Big)^{2}$ $y^{2}+2y+1=-2+1$ $y^{2}+2y+1=-1$ Factor the left side of the equation, which is a perfect square trinomial: $(y+1)^{2}=-1$ Take the square root of both sides of the equation: $\sqrt{(y+1)^{2}}=\sqrt{-1}$ $y+1=\pm i$ Solve for $y$: $y=-1\pm i$
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