Question

Розв'яжіть рівняння: 1) (2х — 1) (15 + 9x) - 6x (3х - 5) = 87;2) (14х — 1) (2 + х) = (2x – 8) (7х + 1);3) (х + 10) (х – 5) - (х – 6) (х + 3) = 16;4) (3х + 7) (8х + 1) = (6x - 7) (4x - 1) + 93x​

Answer 1

Ответ:

1)30х+18хдо квадрату-15-9х-18х до квадрату +30х=87

51х-15=87

51х-15-87=0

х-2=0

х=2

3)х1=6,х2=8

4)3х-56х-7=6х-28х+7+93х

-53х-7=71х+7

-53х-71х=7+7

-124х=14

х=-0,1

Answer 2

1. (2x - 1)(15 + 9x) - 6x(3x - 5) = 87

First, distribute and simplify each term:

(2x - 1)(15) + (2x - 1)(9x) - (6x)(3x) + (6x)(5) = 87

30x - 15 + 18x^2 - 9x - 18x + 30 = 87

Now, combine like terms:

18x^2 + 3x - 15 + 30 - 18x = 87

18x^2 + 3x + 15 - 18x = 87

Now, move all terms to one side to set the equation equal to zero:

18x^2 + 3x + 15 - 18x - 87 = 0

Now, simplify the equation further:

18x^2 - 15 - 87 = 0

18x^2 - 102 = 0

Now, divide by the common factor (6):

3x^2 - 17 = 0

Now, you have a quadratic equation. To solve it, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 3, b = 0, and c = -17. Plug these values into the quadratic formula:

x = (0 ± √(0 - 4(3)(-17))) / (2(3))

x = (± √(204)) / 6

x = (± 2√51) / 6

x = (± √51) / 3

So, the solutions to the equation are:

x = (√51) / 3 and x = (-√51) / 3

2. (14x - 1)(2 + x) = (2x - 8)(7x + 1)

First, distribute and simplify each term:

(14x - 1)(2) + (14x - 1)(x) = (2x - 8)(7x) + (2x - 8)(1)

28x - 2 + 14x^2 - x = 14x^2 - 56x + 2x - 8

Now, combine like terms:

14x^2 + 28x - 2 - x - 14x^2 + 56x - 2x + 8 = 0

14x^2 + 25x + 6 - 14x^2 = 0

Now, simplify the equation further:

25x + 6 = 0

Subtract 6 from both sides:

25x = -6

Now, divide by 25:

x = -6/25

So, the solution to the equation is:

x = -6/25

3. (x + 10)(x - 5) - (x - 6)(x + 3) = 16

First, distribute and simplify each term:

(x^2 - 5x + 10x - 50) - (x^2 + 3x - 6x - 18) = 16

Now, combine like terms:

x^2 + 5x - 50 - x^2 - 3x + 6x + 18 = 16

x^2 + 5x - x^2 - 3x + 6x - 50 + 18 = 16

Now, simplify the equation further:

5x = 16 + 50 - 18

5x = 48

Now, divide by 5:

x = 48/5

So, the solution to the equation is:

x = 48/5

4. (3x + 7)(8x + 1) = (6x - 7)(4x - 1) + 93x

First, distribute and simplify each term:

(24x^2 + 3x + 56x + 7) = (24x^2 - 6x - 28x + 7) + 93x

Now, combine like terms:

(24x^2 + 59x + 7) = (24x^2 + 59x + 7) + 93x

Now, subtract (24x^2 + 59x + 7) from both sides:

0 = 93x

Now, divide by 93:

x = 0

So, the solution to the equation is:

x = 0