`a)x²-11x+3=0`
`⇔x²-11x+121/4-109/4=0`
`⇔x²-11x+121/4=109/4`
`⇔x²-2.x. 11/2+(11/2)^2=109/4`
`⇔(x-11/2)^2=(`$\dfrac{\sqrt[]{109}}{2}$`)^2`
`⇔`$\left[\begin{matrix} x-\dfrac{11}{2}=\dfrac{\sqrt[]{109}}{2}\\ x-\dfrac{11}{2}=-\dfrac{\sqrt[]{109}}{2}\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=\dfrac{\sqrt[]{109}}{2}+\dfrac{11}{2}\\ x=-\dfrac{\sqrt[]{109}}{2}+\dfrac{11}{2}\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=\dfrac{\sqrt[]{109}+11}{2}\\ x=\dfrac{11-\sqrt[]{109}}{2}\end{matrix}\right.$
Vậy `x\in{`$\dfrac{\sqrt[]{109}+11}{2}$`;`$\dfrac{11-\sqrt[]{109}}{2}$`}`
`b)2x²+3x-27=0`
`⇔2x²-6x+9x-27=0`
`⇔2x(x-3)+9(x-3)=0`
`⇔(x-3)(2x+9)=0`
`⇔`$\left[\begin{matrix} x-3=0\\ 2x+9=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=3\\ x=-\dfrac{9}{2}\end{matrix}\right.$
Vậy `x∈{3;-9/2}`
`c)x²-2x-3=0`
`⇔x²-3x+x-3=0`
`⇔x(x-3)+(x-3)=0`
`⇔(x-3)(x+1)=0`
`⇔`$\left[\begin{matrix} x-3=0\\ x+1=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=3\\ x=-1\end{matrix}\right.$
Vậy `x∈{3;-1}`
`d)2x²+5x-3=0`
`⇔2x²-x+6x-3=0`
`⇔x(2x-1)+3(2x-1)=0`
`⇔(2x-1)(x+3)=0`
`⇔`$\left[\begin{matrix} x+3=0\\ 2x-1=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=-3\\ x=\dfrac{1}{2}\end{matrix}\right.$
Vậy `x∈{-3;1/2}`
`e)5x(x-1)=x-1`
`⇔5x(x-1)-(x-1)=0`
`⇔(x-1)(5x-1)=0`
`⇔`$\left[\begin{matrix} x-1=0\\ 5x-1=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=1\\ x=\dfrac{1}{5}\end{matrix}\right.$
Vậy `x∈{1;1/5}`
`f)2(x+5)-x²-5x=0`
`⇔2(x+5)-x(x+5)=0`
`⇔(x+5)(2-x)=0`
`⇔`$\left[\begin{matrix} x+5=0\\ 2-x=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=-5\\ x=2\end{matrix}\right.$
Vậy `x∈{-5;2}`
