1: \(2x\left(x-5\right)-x\left(2x+3\right)=26\)
=>\(2x^2-10x-2x^2-3x=26\)
=>-13x=26
=>\(x=\dfrac{26}{-13}=-2\)
2: \(\left(2x-3\right)^2-\left(x+5\right)^2=0\)
=>\(\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)
=>\(\left(x-8\right)\left(3x+2\right)=0\)
=>\(\left[{}\begin{matrix}x-8=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)
3: \(x^2-64=8x-16\)
=>\(x^2-8x+16-64=0\)
=>\(x^2-8x-48=0\)
=>(x-12)(x+4)=0
=>\(\left[{}\begin{matrix}x-12=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=12\\x=-4\end{matrix}\right.\)
4: \(5x\left(x-1\right)=x-1\)
=>\(5x\left(x-1\right)-\left(x-1\right)=0\)
=>(x-1)(5x-1)=0
=>\(\left[{}\begin{matrix}x-1=0\\5x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{5}\end{matrix}\right.\)
5: \(3x^3-48x=0\)
=>\(3x\left(x^2-16\right)=0\)
=>\(x\left(x^2-16\right)=0\)
=>\(x\cdot\left(x-4\right)\left(x+4\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
6: \(x^2-x-6=0\)
=>\(x^2-3x+2x-6=0\)
=>\(x\left(x-3\right)+2\left(x-3\right)=0\)
=>\(\left(x-3\right)\left(x+2\right)=0\)
=>\(\left[{}\begin{matrix}x-3=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
7: \(2\left(x+5\right)-x^2-5x=0\)
=>\(2\left(x+5\right)-\left(x^2+5x\right)=0\)
=>\(2\left(x+5\right)-x\left(x+5\right)=0\)
=>(x+5)(2-x)=0
=>\(\left[{}\begin{matrix}x+5=0\\2-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
8: \(x^3+x^2-4x=4\)
=>\(x^3+x^2-4x-4=0\)
=>\(x^2\left(x+1\right)-4\left(x+1\right)=0\)
=>\(\left(x+1\right)\left(x^2-4\right)=0\)
=>\(\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)
=>\(\left[{}\begin{matrix}x+1=0\\x-2=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\\x=-2\end{matrix}\right.\)
9: \(x^5=x^3\)
=>\(x^5-x^3=0\)
=>\(x^3\left(x^2-1\right)=0\)
=>\(x^3\left(x-1\right)\left(x+1\right)=0\)
=>\(\left[{}\begin{matrix}x^3=0\\x-1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
