Question

Solve by Factoring:
4z^2 - 4z +1 = 0

Answer 1

I'm having a little trouble getting past the first step. So far I have:
4z^2 - 4z = -1
but maybe it's supposed to start off with
4(z^2 - z) +1 = 0?

Answer 2

you have to factor the equation...

(Hint: you have a perfect square polynomial
in the form of a²-2ab+b²=(a-b)² )

Answer 3

\(\color{#000000 }{ \displaystyle 4z^2-4z+1\quad\Longrightarrow\quad (2z)^2-2(2z)(1)+(1)^2 }\)
\(\tiny{\\[1.5em]}\)
\(\color{#000000 }{ \displaystyle (2z)^2-2(2z)(1)+(1)^2\quad\Longrightarrow\quad (2z-1)^2}\)\(\tiny{\\[1.3em]}\)
\(\color{#000000 }{ \displaystyle (a)^2-2(a)(b)+(b)^2\quad\Longrightarrow\quad (a-b)^2}\)

Answer 4

So,
\(\color{#000000 }{ \displaystyle 4z^2-4z+1=(2z-1)^2 }\)

Answer 5

Now, you have,
\(\color{#000000 }{ \displaystyle (2z-1)^2=0 }\)

Solve for \(\color{black}{z}\)...

Answer 6

2z = 1
z = 1/2

Answer 7

thanks!