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