Đáp án:
$a. ( x - 1 )^{2} + x( 4 - x ) = 11$
⇔ $x^{2} - 2x + 1 + 4x - x^{2} = 11$
⇔ $2x + 1 = 11$
⇔ $2x = 10$
⇔ $x = 5$
$b. ( x - 5 )^{2} - x( x + 2 ) = 5$
⇔ $x^{2} - 10x + 25 - x^{2} - 2x = 5$
⇔ $- 12x + 25 = 5$
⇔ $- 12x = - 20$
⇔ $x = \frac{5}{3}$
$c. x( x + 4 ) - x^{2} - 6x = 10$
⇔ $x^{2} + 4x - x^{2} - 6x = 10$
⇔ $- 2x = 10$
⇔ $x = - 5$
$d. 6x^{2} - ( 2x - 3 )( 3x + 2 ) = 1$
⇔ $6x^{2} - 6x^{2} - 4x + 9x + 6 = 1$
⇔ $5x + 6 = 1$
⇔ $5x = - 5$
⇔ $x = - 1$
$e. ( x + 2 )( x - 5 ) + x( 1 - x ) = 2$
⇔ $x^{2} - 5x + 2x - 10 + x - x^{2} = 2$
⇔ $- 2x - 10 = 2$
⇔ $- 2x = 12$
⇔ $x = - 6$
$f. ( x - 1 )( 2 - x ) + ( x - 3 )^{2} = 4 - 2x$
⇔ $2x - x^{2} - 2 + x + x^{2} - 6x + 9 = 4 - 2x$
⇔ $- 3x + 7 = 4 - 2x$
⇔ $- x = - 3$
⇔ $x = 3$
