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: 42

Answer

$x=(3+\sqrt 6, 3-\sqrt 6)$

Work Step by Step

Step-1 : Subtract $3$ on both sides of the equation $x^2-6x=-3$ 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 $x^2-6x+9=-3+9$ Step-3 Factor the trinomial and simplify the right hand side. $(x-3)^2=6$ Step-4 Use the square root property and solve for $x$ $(x-3)=±\sqrt 6 $ Step-5 Add 3 on both the sides $x=3±\sqrt 6$ Therefore the solution set is $(3+\sqrt 6, 3-\sqrt 6)$
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