Đáp án + Giải thích các bước giải:

`a)`

`9x^{2}-6x-3=0`

`<=>(9x^{2}-6x+1)-4=0`

`<=>(3x-1)^{2}-2^{2}=0`

`<=>(3x-1-2)(3x-1+2)=0`

`<=>(3x-3)(3x+1)=0`

`<=>` \(\left[ \begin{array}{l}3x-3=0\\3x+1=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=1\\x=-\dfrac{1}{3}\end{array} \right.\) 

Vậy `S={1;-(1)/(3)}`

`b)`

`x^{3}+9x^{2}+27x+19=0`

`<=>(x^{3}+9x^{2}+27x+27)-8=0`

`<=>(x+3)^{3}-2^{3}=0`

`<=>(x+3-2)[(x+3)^{2}+2(x+3)+4]=0`

`<=>(x+1)(x^{2}+6x+9+2x+6+4)=0`

`<=>(x+1)(x^{2}+8x+19)=0`

`<=>x+1=0` ( Vì `x^{2}+8x+19=(x+4)^{2}+3>0` với mọi `x` )

`<=>x=-1`

Vậy `S={-1}`

`c)`

`x(x+5)(x-5)-(x+2)(x^{2}-2x+4)=3`

`<=>x(x^{2}-25)-(x^{3}+8)=3`

`<=>x^{3}-25x-x^{3}-8=3`

`<=>-25x-8=3`

`<=>-25x=11`

`<=>x=-(11)/(25)`

Vậy `S={-(11)/(25)}`

`d)`

`x^{2}-4x+4=25`

`<=>(x-2)^{2}-5^{2}=0`

`<=>(x-2-5)(x-2+5)=0`

`<=>(x-7)(x+3)=0`

`<=>` \(\left[ \begin{array}{l}x-7=0\\x+3=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=7\\x=-3\end{array} \right.\) 

Vậy `S={7;-3}`

`a)9x^2-6x-3=0`

`⇔(3x)^2-2.3x.1+1-4=0`

`⇔(3x-1)^2-4=0`

`⇔(3x-1-2)(3x-1+2)=0`

`⇔3x-3=0` hoặc `3x+1=0`

`⇔x=1` hoặc `x=-1/3`

Vậy `S={1;-1/3}`

`b)x^3+9x^2+27x+19=0`

`⇔x^3+3.3.x^2+3.3^2.x+3^3-8=0`

`⇔(x+3)^3-2^3=0`

`⇔(x+3-2)(x^2+6x+9+2x+6+4)=0`

`⇔x+1=0` (Vì `x^2+6x+9+2x+6+4=x^2+8x+19=(x+4)^2+3>=3)`

`⇔x=-1`

Vậy `S={-1}`

`c)x(x+5)(x-5)-(x+2)(x^2-2x+4)=3`

`⇔x(x^2-25)-(x^3+8)=3`

`⇔x^3-25x-x^3-8=3`

`⇔-25x-8=3`

`⇔-25x=11`

`⇔x=(11)/(-25)`

Vậy `S={(11)/(-25)}`

`a)x^2-4x+4=25`

`⇔(x-2)^2-5^2=0`

`⇔(x-2-5)(x-2+5)=0`

`⇔x-7=0` hoặc `x+3=0`

`⇔x=7` hoặc `x=-3`

Vậy` S={7;-3}`