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: 41

Answer

$x=(-1+\sqrt 6, -1-\sqrt 6)$

Work Step by Step

Step-1 : Add $5$ on both sides of the equation $x^2+2x=5$ Step -2 : Add the square of half of the co-efficient of $x$ to both sides. Co-efficient of $x =2$ Half of $2 = \frac{1}{2}×2=1$ Square of $1$ is $1×1=1$ The equation becomes $x^2+2x+1=5+1$ Step-3 Factor the trinomial and simplify the right hand side. $(x+1)^2=6$ Step-4 Use the square root property and solve for $x$ $(x+1)=±\sqrt 6 $ Step-5 Subtract 1 on both the sides $x=-1±\sqrt 6$ Therefore the solution set is $(-1+\sqrt 6, -1-\sqrt 6)$
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