Đáp án:
a/ `x = - \frac{1}{8}`
b/ `x = - \frac{1}{8}`
c/ `x =-\frac{255}{2}`
d/ `x = -6`

Giải thích các bước giải:
a/ `25x^2 - 160 =9`
`<=> 25x^2 - 169 = 0`
`<=> ( 5x - 13 )( 5x + 13 ) = 0`
`<=>` \(\left[ \begin{array}{l}5x - 13 = 0\\5x + 13 = 0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac{13}{5}\\x=-\dfrac{13}{5}\end{array} \right.\)
b/ `( x + 4 )^2 - ( x -1)( x + 1 ) = 16`
`<=> x^2 + 8x + 16 - x^2 + 1  = 16`
`<=> 8x = -1`
`<=> x = - \frac{1}{8}`
c/ `( 2x - 1 )^2 + ( x + 3 )^2 - 5( x - 7 )( x + 7 ) = 0`
`<=> 4x^2 - 4x + 1 + x^2 + 6x + 9 - 5( x^2 - 49 ) = 0`
`<=> 4x^2 - 4x + 1 + x^2 + 6x + 9 - 5x^2 + 245 =0`
`<=> 2x = -255`
`<=> x =-\frac{255}{2}`
d/ `( x- 2)^2 - 4( x^2 - 4 ) + 4( x + 2 )^2 = 0`
` <=> [ ( x - 2 ) - 2( x + 2 ) ]^2 = 0`
`<=> ( x - 2 - 2x - 4 )^2 = 0`
`<=> ( -x - 6 )^2= 0` 
`<=> x = -6`

`a, 25x^2 - 160 = 9`

`⇔ 25x^2 = 169`

`⇔ x^2 = 169/25`

`⇔ x = ± 13/5`

`b, (x+4)^2 - (x-1)(x+1) = 16`

`⇔ x^2 + 8x + 16 - x^2 + 1 = 16`

`⇔ 8x = -1`

`⇔ x = -1/8`

`c, (2x - 1)^2 + (x+3)^2 - 5(x-7)(x+7) = 0`

`⇔ 4x^2 - 4x + 1 + x^2 + 6x + 9 - 5(x^2 - 49) = 0`

`⇔ 5x^2 + 2x + 10 - 5x^2 + 245 = 0`

`⇔ 2x = -255`

`⇔ x = -255/2`

`d, (x-2)^2 - 4(x^2 - 4) + 4(x + 2)^2 = 0`

`⇔ x^2 - 4x + 4 - 4x^2 + 16 + 4(x^2 + 4x + 4) = 0`

`⇔ -3x^2 - 4x + 20 + 4x^2 + 16x + 16 = 0`

`⇔ x^2 + 12x + 36 = 0`

`⇔ (x + 6)^2 = 0`

`⇔ x + 6 = 0`

`⇔ x = -6`