Giải thích các bước giải:

 1, `5(x+3)-4x(3+x)=0`

`=>(5-4x)(x+3)=0`

`=>`\(\left[ \begin{array}{l}5-4x=0\\x+3=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=\dfrac54\\x=-3\end{array} \right.\)

 2, `4x(x-2004)-x+2004=0`

`=>4x(x-2004)-(x-2004)=0`

`=>(4x-1)(x-2004)=0`

`=>`\(\left[ \begin{array}{l}4x-1=0\\x-2004=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=\dfrac14\\x=2004\end{array} \right.\)

 3, `x^2+8x+16=0`

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

`=>x+4=0`

`=>x=-4`

 4, `4x^2-12x=-9`

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

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

`=>2x-3=0`

`=>x=3/2`

Đáp án:

Giải thích các bước giải:

`1) 5.(x + 3) - 4x.(3 + x) = 0.`

`⇒ 5.(x + 3) - 4x.(x + 3) = 0.`

`⇒ (5 - 4x).(x + 3) = 0.`

`⇒` \(\left[ \begin{array}{l}5-4x=0.\\x+3=0.\end{array} \right.\)

`⇒` \(\left[ \begin{array}{l}4x=5.\\x=-3.\end{array} \right.\)

`⇒` \(\left[ \begin{array}{l}x=\dfrac{5}{4}.\\x=-3.\end{array} \right.\)

Vậy `x=5/4` hoặc `x=-3.`

`2) 4x.(x - 2004) - x + 2004 = 0.`

`⇒ 4x.(x - 2004) - (x - 2004) = 0.`

`⇒ (4x - 1).(x - 2004) = 0.`

`⇒` \(\left[ \begin{array}{l}4x-1=0.\\x-2004=0.\end{array} \right.\)

`⇒` \(\left[ \begin{array}{l}4x=1.\\x=2004.\end{array} \right.\)

`⇒` \(\left[ \begin{array}{l}x=\dfrac{1}{4}.\\x=2004.\end{array} \right.\)

Vậy `x = 1/4` hoặc `x = 2004.`

`3) x^2 + 8x + 16 = 0.`

`⇒ x^2 + 2.x.4 + 4^2 = 0.`

`⇒ (x + 4)^2 = 0.`

`⇒ x + 4 = 0.`

`⇒ x = -4.`

Vậy `x = -4.`

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

`⇒ 4x^2 - 12x + 9 = 0.`

`⇒ (2x)^2 - 2.2x.3 + 3^2 = 0.`

`⇒ (2x - 3)^2 = 0.`

`⇒ 2x - 3 = 0.`

`⇒ 2x = 3.`

`⇒ x = 3/2.`

$\text{Vậy x = $\dfrac{3}{2}$.}$

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