`a) (x-4)^2-36=0`

`<=> (x-4)^2-6^2=0`

`<=> (x-4-6)(x-4+6)=0`

`<=> (x-10)(x+2)=0`

`<=>`\(\left[ \begin{array}{l}x-10=0\\x+2=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=10\\x=-2\end{array} \right.\) 

`b) (x+8)^2=121`

`<=> (x+8)^2-11^2=0`

`<=> (x+8-11)(x+8+11)=0`

`<=> (x-3)(x+19)=0`

`<=>`\(\left[ \begin{array}{l}x-3=0\\x+19=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=3\\x=-19\end{array} \right.\) 

`c) x^2+8x+16=0`

`<=> x^2+2.x.4+4^2=0`

`<=> (x+4)^2=0`

`<=> x+4=0`

`<=> x=-4`

`d) 4x^2-12x=-9`

`<=> 4x^2-12x+9=0`

`<=> (2x)^2-2.2x.3+3^2=0`

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

`<=> 2x-3=0`

`<=> x=3/2`

 

$(x - 4)^{2}$ - 36 = 0

<=> $(x - 4)^{2}$ - $6^{2}$ = 0

<=> (x - 4 - 6)(x - 4 + 6) = 0

<=> (x - 10)(x + 2) = 0

<=>  $\left \{ {{x - 10 = 0} \atop {x + 2 = 0}} \right.$  

<=>\(\left[ \begin{array}{l}x=10\\x=-2\end{array} \right.\) 

Vậy x = { -2 ; 10 }

b, $(x + 8)^{2}$ = 121

<=> $\left \{ {{x + 8=11} \atop {x + 8= -11}} \right.$ 

<=> \(\left[ \begin{array}{l}x=3\\x=-19\end{array} \right.\) 

Vậy x = { 3 ; -19}

c, $x^{2}$ + 8x + 16 = 0

<=> $x^{2}$ + 2. 4x + $4^{2}$ = 0

<=> $(x + 4)^{2}$  = 0 => x = -4

Vậy x = -4

d, $4x^{2}$ - 12x = -9

<=> $4x^{2}$ - 12x + 9 = 0

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

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

=> x = $\frac{3}{2}$