Question

(3 x+1)(5x-3)+(9x^2+6x+1)=0​

Answer 1

Ответ:

x₁=1/4, х₂= -1/3

Пошаговое объяснение:

(3x+1)(5x-3)+(9x²+6x+1)=0​

15x²- 9x+5x-3+9x²+6x+1=0

24x²+2x-2=0

12x²+x-1=0

D=b²-4ac ⇒1-4*12*(-1)=1+48=√49=7

x₁= -1+7/12*2=1/4=0,25

х₂= -1-7/12*2= -1/3

Answer 2

To solve the equation (3x + 1)(5x - 3) + (9x^2 + 6x + 1) = 0, follow these steps:

1. Expand the expressions on the left side of the equation: (3x + 1)(5x - 3) + (9x^2 + 6x + 1) = 0 (15x^2 - 9x + 5x - 3) + (9x^2 + 6x + 1) = 0

2. Combine like terms: 15x^2 - 9x + 5x - 3 + 9x^2 + 6x + 1 = 0

3. Simplify the equation by combining like terms: 24x^2 + 2x - 2 = 0

4. Now, you have a quadratic equation in the form ax^2 + bx + c = 0, where: a = 24 b = 2 c = -2

5. To solve this quadratic equation, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

   Plugging in the values: x = (-2 ± √(2² - 4(24)(-2))) / (2 * 24)

6. Calculate the discriminant (the value inside the square root): Discriminant = 2² - 4(24)(-2) = 4 + 192 = 196

7. Now, use the quadratic formula to find the solutions for x: x = (-2 ± √196) / (2 * 24)

   Simplify further: x = (-2 ± 14) / 48

8. Split the equation into two separate solutions: a) x = (-2 + 14) / 48 b) x = (-2 - 14) / 48

9. Calculate each solution: a) x = 12 / 48 = 1/4 b) x = -16 / 48 = -1/3

So, the solutions to the equation (3x + 1)(5x - 3) + (9x^2 + 6x + 1) = 0 are: x = 1/4 and x = -1/3.