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: 15

Answer

x=6

Work Step by Step

The coefficient of x is -10. Adding the square of half the coefficient of x creates a perfect square. $(-10\div2)^2=(-5)^2=25$ $x^2-10x=-24$ Add the square of half the coefficient of x to each side of the equation. $x^2-10x+25=-24+25$ Simplify. $x^2-10x+25=1$ Factor the polynomial. $(x-5)^2=1$ Take the square root of each side. $\sqrt{(x-5)^2}=\sqrt 1$ Simplify. $x-5=1$ Add 5 to each side. $x-5+5=1+5$ Simplify. $x=6$
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