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: 62


$y=1$ and $y=-2$

Work Step by Step

$y^{2}+y-2=0$ Take the $2$ to the right side of the equation: $y^{2}+y=2$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this case, $b=1$ $y^{2}+y+\Big(\dfrac{1}{2}\Big)^{2}=2+\Big(\dfrac{1}{2}\Big)^{2}$ $y^{2}+y+\dfrac{1}{4}=\dfrac{9}{4}$ Factor the expression on the left side of the equation, which is a perfect square trinomial: $\Big(y+\dfrac{1}{2}\Big)^{2}=\dfrac{9}{4}$ Take the square root of both sides of the equation: $\sqrt{\Big(y+\dfrac{1}{2}\Big)^{2}}=\sqrt{\dfrac{9}{4}}$ $y+\dfrac{1}{2}=\pm\dfrac{3}{2}$ Solve for $y$: $y=\dfrac{-1\pm3}{2}$ The two solutions are: $y=\dfrac{-1+3}{2}=1$ $y=\dfrac{-1-3}{2}=-2$
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