№2. Решите уравнения: 1. 2 + 9x = 4x + 3. 2. x² + 10x = −16. 3. x² + 3x = 0. 4. x² = 7x + 8. 5. x² − 81 = 0. 6. x² − 36 = 0. 7. 16x² − 1 = 0. 8. 4x − 5x² = 0. 9. x² = 7x. 10. 3x² − 5x − 2 = 0.

1. \(2+9x=4x+3\); \(9x-4x=3-2\); \(5x=1\); \(x=\frac{1}{5}\).
2. \(x^2+10x=-16\); \(x^2+10x+16=0\); \((x+2)(x+8)=0\); \(x_1=-2,\ x_2=-8\).
3. \(x^2+3x=0\); \(x(x+3)=0\); \(x_1=0,\ x_2=-3\).
4. \(x^2=7x+8\); \(x^2-7x-8=0\); \((x-8)(x+1)=0\); \(x_1=8,\ x_2=-1\).
5. \(x^2-81=0\); \((x-9)(x+9)=0\); \(x_1=9,\ x_2=-9\).
6. \(x^2-36=0\); \((x-6)(x+6)=0\); \(x_1=6,\ x_2=-6\).
7. \(16x^2-1=0\); \((4x-1)(4x+1)=0\); \(x_1=\frac14,\ x_2=-\frac14\).
8. \(4x-5x^2=0\); \(x(4-5x)=0\); \(x_1=0,\ x_2=\frac45\).
9. \(x^2=7x\); \(x^2-7x=0\); \(x(x-7)=0\); \(x_1=0,\ x_2=7\).
10. \(3x^2-5x-2=0\); \(D=(-5)^2-4\cdot3\cdot(-2)=49\); \(x=\frac{5\pm7}{6}\); \(x_1=2,\ x_2=-\frac13\).

Ответ: 1) x=1/5; 2) x=−2, −8; 3) x=0, −3; 4) x=8, −1; 5) x=±9; 6) x=±6; 7) x=±1/4; 8) x=0, 4/5; 9) x=0, 7; 10) x=2, −1/3.