## College Algebra (6th Edition)

Published by Pearson

# Chapter 1 - Equations and Inequalities - Exercise Set 1.5 - Page 160: 14

#### Answer

$x=\frac{1}{2},1$

#### Work Step by Step

FOIL the right side and combine like terms, and then get all the numbers on one side to make the other side zero. Then find the GCF of the terms, and in the parentheses multiply the coefficient of the first term by the third term and then do trial and error. Then group and find the greatest common factors of each group to get the complete factorization. Then solve for $x$ by setting each value equal to zero. $10x-1=(2x+1)^2$ $10x-1=(2x+1)(2x+1)$ $10x-1=4x^2+2x+2x+1$ $10x-1=4x^2+4x+1$ $10x-1-4x^2-4x-1=0$ $-4x^2+6x-2=0$ $-2(2x^2-3x+1)=0$ $-2(2x^2-2x-x+1)=0$ $-2(2x(x-1)-1(x-1)=0$ $-2(2x-1)(x-1)=0$ $-2\ne0$ $2x-1=0$ $2x=1$ $x=\frac{1}{2}$ $x-1=0$ $x=1$ $x=\frac{1}{2},1$

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