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: 46

Answer

$x = (5+\sqrt 23, 5-\sqrt 23)$

Work Step by Step

Step-1 : Subtract $2$ on both sides of the equation $x^2-10x=-2$ Step -2 : Add the square of half of the co-efficient of $x$ to both sides. Co-efficient of $x =-10$ Half of $-10 = \frac{1}{2}×-10=-5$ Square of $-5$ is $-5×-5=25$ The equation becomes $x^2-10x+25=-2+25$ Step-3 Factor the trinomial and simplify the right hand side. $(x-5)^2=23$ Step-4 Use the square root property and solve for $x$ $(x-5)=±\sqrt 23 $ Step-5 Add 5 on both the sides $x=5±\sqrt 23$ Therefore the solution set is $(5+\sqrt 23, 5-\sqrt 23)$
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