College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 21


$x=\left\{ \dfrac{1}{2} \right\}$

Work Step by Step

The two numbers whose product is $ac= 4(1)=4 $ and whose sum is $b= -4 $ are $\{ -2,-2 \}$. Using these two numbers to decompose the middle term of the given equation, $ 4x^2-4x+1=0 ,$ results to \begin{array}{l}\require{cancel} 4x^2-2x-2x+1=0 \\\\ (4x^2-2x)-(2x-1)=0 \\\\ 2x(2x-1)-(2x-1)=0 \\\\ (2x-1)(2x-1)=0 .\end{array} Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are \begin{array}{l}\require{cancel} 2x-1=0 \\\\ 2x=1 \\\\ x=\dfrac{1}{2} ,\\\\\text{OR}\\\\ 2x-1=0 \\\\ 2x=1 \\\\ x=\dfrac{1}{2} .\end{array} Hence, the solution is $ x=\left\{ \dfrac{1}{2} \right\} .$
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