a.
\(x^2-16x=0\)
\(\Leftrightarrow x\left(x-16\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=16\end{matrix}\right.\)
b.
\(9x^2+6x+4y^2-8y+5=0\)
\(\Leftrightarrow\left(9x^2+6x+1\right)+\left(4y^2-8y+4\right)=0\)
\(\Leftrightarrow\left(3x+1\right)^2+\left(2y-2\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+1=0\\2x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=1\end{matrix}\right.\)
\(a,x^2-16x=0\)
\(\Leftrightarrow x\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
\(b,9x^2+6x+4y^2-8y+5=0\)
\(\Leftrightarrow\left(9x^2+6x+1\right)+4\left(y^2-2y+1\right)=0\)
\(\Leftrightarrow\left(3x+1\right)^2+4\left(y-1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(3x+1\right)^2=0\\4\left(y-1\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{3}\\y=1\end{matrix}\right.\)
