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: 37

Answer

$x = (−3-\sqrt 7, −3+\sqrt 7)$

Work Step by Step

Step-1 : Subtract $2$ from both sides of the equation $x^2+6x=-2$ Step -2 : Add the square of half of the co-efficient of $x$ to both sides. Co-efficient of $x = 6$ Half of $6 = \frac{1}{2}×6=3$ Square of $3$ is $3×3=9$ The equation becomes $x^2+6x+9=-2+9$ Step-3 Factor the trinomial and simplify the right hand side. $(x+3)^2=7$ Step-4 Use the square root property and solve for $x$ $(x+3)=±\sqrt 7$ Step-5 Subtract 3 on both the sides $x=−3±\sqrt 7$ Therefore the solution set is $(−3-\sqrt 7, −3+\sqrt 7)$
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