Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.2 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 638: 17


$1+\sqrt6$ or $1-\sqrt6$

Work Step by Step

The coefficient of x is -2. Adding the square of half the coefficient of x creates a perfect square. $(-2\div2)^2=(-1)^2=1$ $x^2-2x=5$ Add the square of half the coefficient of x to each side of the equation. $x^2-2x+1=5+1$ Simplify. $x^2-2x+1=6$ Factor the polynomial. $(x-1)^2=6$ Take the square root of each side. $\sqrt{(x-1)^2}=\sqrt 6$ Simplify. $x-1=\pm \sqrt 6$ Add 1 to each side. $x-1+1=\pm \sqrt 6+1$ Simplify. $x=1+\sqrt6$ or $x=1-\sqrt6$
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