a) \(49x^2-1=0\)
\(\Leftrightarrow\left(7x-1\right)\left(7x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}\\x=-\dfrac{1}{7}\end{matrix}\right.\)
b) \(\left(2x-1\right)^2-\left(4x+1\right)\left(x-3\right)=-3\)
\(\Leftrightarrow4x^2-4x+1-4x^2+11x+3=-3\)
\(\Leftrightarrow7x=-7\Leftrightarrow x=-1\)
c) \(\Leftrightarrow9x^2-9x-9x^2+6x-1=11\)
\(\Leftrightarrow-3x=12\Leftrightarrow x=-4\)
d) \(\Leftrightarrow4x^2+12x+9-x^2+2x-1=0\)
\(\Leftrightarrow3x^2+14x+8=0\)
\(\Leftrightarrow\left(3x+2\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\x=-4\end{matrix}\right.\)
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