Giải phương trình

1.x(2x-1)+5(2x-1)=0

2. X2-9-(x+3)(3x+1)=0

3. X2-10x+25=3(5-x)

4.4x2=(x-12)2

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`1) x(2x - 1) + 5(2x - 1) = 0 `

`(x+5)(2x - 1) = 0 `

`x + 5 = 0 ` hoặc `2x - 1 =0  `

TH1 `: x + 5 = 0 `

`x = - 5 `

TH2 `: 2x - 1 = 0 `

`2x = 1 `

`x = 1/2 `

Vậy `x \in {-5 ; 1/2} `

`2) x^2 - 9 - (x+3)(3x + 1) = 0 `

`x^2 - 3^2 - (x+3)(3x + 1) = 0 `

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

`(x+3)[(x-3) - (3x + 1)] = 0 `

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

`(x+3)(-2x - 4) = 0 `

`x + 3 = 0 ` hoặc `-2x - 4 = 0 `

TH1 `: x + 3 = 0 `

`x = -3 `

TH2 `: -2x - 4 = 0 `

`-2x = 4 `

`x = -2 `

Vậy `x \in {-3 ; -2} `

`3) x^2 - 10x + 25 = 3(5 - x) `

`x^2 - 10x + 25  = 15 - 3x `

`x^2 - 10x + 3x + 25 - 15 =  0`

`x^2 - 7x + 10 = 0 `

`x^2 - 2x - 5x + 10 = 0 `

`(x^2 - 2x) - (5x - 10) = 0 `

`x(x-2) - 5(x-2) = 0 `

`(x-5)(x-2) = 0 `

`x - 5 = 0 ` hoặc `x-2=0` 

TH1 `: x - 5 = 0 `

`x = 5 `

TH2 `: x- 2=0 `

`x = 2 `

Vậy `x \in {5 ; 2} `

`4) 4x^2 = (x-12)^2 `

`4x^2 = x^2 - 2 . x . 12 + 12^2 `

`4x^2 = x^2 - 24x + 144 `

`4x^2 - x^2 + 24x - 144 = 0 `

`3x^2 + 24x - 144 = 0 `

`x^2 + 8x - 48 = 0 `

`x^2 - 4x + 12x - 48 = 0 `

`(x^2 - 4x) + (12x - 48) = 0 `

`x(x - 4) + 12(x-4) = 0 `

`(x+12)(x-4) = 0 `

`x + 12 = 0 ` hoặc `x - 4 = 0 `

TH1 `: x + 12= 0`

`x = -12 `

TH2 `: x-  4 = 0 `

`x = 4 `

Vậy `x \in {-12 ; 4} `