Giải:

a) \(x^2-x+\dfrac{1}{4}=0\)

\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=0\)

\(\Leftrightarrow x-\dfrac{1}{2}=0\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

b) \(4x^2-3=0\)

\(\Leftrightarrow4x^2=3\)

\(\Leftrightarrow x^2=\dfrac{3}{4}\)

\(\Leftrightarrow x=\pm\sqrt{\dfrac{3}{4}}\)

c) \(x^2-1=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)

d) \(x^2+4x+4=0\)

\(\Leftrightarrow\left(x+2\right)^2=0\)

\(\Leftrightarrow x+2=0\)

\(\Leftrightarrow x=-2\)

Chúc bạn học tốt!