Question

1. (x+1)²-9(x+6)(x-1)=7(x+3)²-8

Answer 1

x²+2x+1-9x(x-1)-54(x-1)=7x²+42x+63-8
x²+2x+1-9x²+9x-54x+54-7x²-42x-55=0
-15x²-85x=0 ÷(-5)
3x²+17x=0 ⇒ x(3x+17)=0 ⇒
x₁=0 x₂=-17/3

Answer 2

${(x + 1)}^{2} - 9(x + 6)(x - 1) = 7 {(x + 3)}^{2} - 8$

${x}^{2} + 2x + 1 - 9( {x}^{2} - x + 6x - 6) = 7( {x}^{2} + 6x + 9) - 8$

${x}^{2} + 2x + 1 - 9( {x}^{2} + 5x - 6) = 7 {x}^{2} + 42x + 63 - 8$

${x}^{2} + 2x + 1 - 9 {x}^{2} - 45x + 54 = 7 {x}^{2} + 42x + 63 - 8$

${x}^{2} - 9 {x}^{2} - 7 {x}^{2} + 2x - 45x - 42x + 1 + 54 - 63 + 8 = 0$

$- 15 {x}^{2} - 85x + 0 = 0$

$- 15 {x}^{2} - 85x = 0$

$a = - 15$

$b = - 85$

$c = 0$

$\Delta = {b}^{2} - 4ac$

$\Delta = {( - 85)}^{2} - 4 \times ( - 15) \times 0$

$\Delta = 7225\:>0\:=>\:\exists\:x_{1}\:\neq\:x_{2}$

$x_{1,2} = \frac{ - b \pm \sqrt{\Delta} }{2a} = \frac{ - ( - 85) \pm \sqrt{7225} }{2 \times ( - 15)} = \frac{85 \pm85}{ - 30}$

$x_{1} = \frac{85 + 85}{ -30} = - \frac{85 + 85}{30} = - \frac{170}{30} = - \frac{17}{3}$

$x_{2} = \frac{85 - 85}{ - 30} = - \frac{85 - 85}{30} = - \frac{0}{30} = 0$