a: \(x^2-2x=-1\)
=>\(x^2-2x+1=0\)
=>\(\left(x-1\right)^2=0\)
=>x-1=0
=>x=1
b: \(x^2=4x\)
=>\(x^2-4x=0\)
=>x(x-4)=0
=>\(\left[\begin{array}{l}x=0\\ x-4=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=4\end{array}\right.\)
c: \(x\left(x+1\right)-\left(x-1\right)^2=x+5\)
=>\(x^2+x-\left(x^2-2x+1\right)=x+5\)
=>\(x^2+x-x^2+2x-1=x+5\)
=>3x-1=x+5
=>2x=6
=>x=3
d: \(\left(x+1\right)\left(x^2-x+1\right)-x^2\left(x+2\right)+2x^2-x+3=0\)
=>\(x^3+1-x^3-2x^2+2x^2-x+3=0\)
=>4-x=0
=>x=4
e: \(\left(x+2\right)\left(x-3\right)-\left(x-1\right)\left(x+3\right)=5\)
=>\(x^2-3x+2x-6-\left(x^2+2x-x-3\right)=5\)
=>\(x^2-x-6-\left(x^2+x-3\right)=5\)
=>\(x^2-x-6-x^2-x+3=5\)
=>-2x-3=5
=>-2x=8
=>x=-4
