Question

2)(3,5-х)(7х+2)+(3,5х-1)(7+2х)=-450 3)(8x+3)(1-0,9x)+7,4=(4x-5)(1-1,8x) 4)498+(2,7-5x)(6x-7)=(9-0,5x)(60x+1)

Answer 1

1. 24.5x+7-7x^2-2x+24.5x+7x^2-7-2x=-450 ( 7 и 7x^2 сократились)

45x=-450

x= -10

2. 8x-7.2x^2+3-2.7x+7.4=4x-7.2x^2-5+9x

5.6x+10.4=13x-5

5.3x-13x=-5-10.4

-7.7x=-15.4

x=2

3. не правильно записано

Answer 2

To solve each of these equations, we need to simplify the expressions, set them equal to zero, and then solve for the variable 'x'. Let's go through each of them step by step:

1. (3.5 - x)(7x + 2) + (3.5x - 1)(7 + 2x) = -450

Step 1: Expand the expressions: (3.5 * 7x) + (3.5 * 2) - (x * 7x) - (x * 2) + (3.5x * 7) + (3.5x * 2x) - (1 * 7) - (1 * 2x) = -450

Step 2: Combine like terms: 24.5x + 7 - 7x^2 - 2x + 24.5x^2 - 7 - 2x = -450

Step 3: Simplify: 24.5x + 7 - 7x^2 - 2x + 24.5x^2 - 7 - 2x + 450 = 0

Step 4: Combine like terms again: 24.5x^2 + 20.5x + 450 = 0

Now, the equation is in standard quadratic form (ax^2 + bx + c = 0), and we can use the quadratic formula to solve for 'x':

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 24.5, b = 20.5, and c = 450.

Calculate: x = (-(20.5) ± √((20.5)^2 - 4 * 24.5 * 450)) / (2 * 24.5)

x = (-20.5 ± √(420.25 - 44100)) / 49

x = (-20.5 ± √(-43679.75)) / 49

Since the discriminant (the value inside the square root) is negative, the equation has no real solutions. Therefore, there is no real value of 'x' that satisfies the equation.

2. (8x + 3)(1 - 0.9x) + 7.4 = (4x - 5)(1 - 1.8x)

Step 1: Expand the expressions: (8x * 1) + (8x * (-0.9)) + (3 * 1) + (3 * (-0.9x)) + 7.4 = (4x * 1) + (4x * (-1.8)) + (-5 * 1) + (-5 * (-1.8x))

Step 2: Combine like terms: 8x - 7.2x + 3 - 2.7x + 7.4 = 4x - 7.2x - 5 + 9x

Step 3: Simplify: 8x - 7.2x - 2.7x - 4x + 9x + 3 + 7.4 + 5 = 0

Step 4: Combine like terms: 3.1x + 15.4 = 0

Step 5: Move constant term to the other side: 3.1x = -15.4

Step 6: Solve for 'x': x = -15.4 / 3.1 x = -5

So, the solution for this equation is 'x = -5'.

3. 498 + (2.7 - 5x)(6x - 7) = (9 - 0.5x)(60x + 1)

Step 1: Expand the expressions: 498 + (2.7 * 6x) - (2.7 * 7) - (5x * 6x) + (5x * 7) = (9 * 60x) + (9 * 1) - (0.5x * 60x) - (0.5x * 1)

Step 2: Combine like terms: 498 + 16.2x - 18.9 - 30x^2 + 35x = 540x + 9 - 30x^2 - 0.5x

Step 3: Simplify: 498 + 16.2x - 18.9 - 30x^2 + 35x - 540x - 9 + 30x^2 + 0.5x = 0

Step 4: Combine like terms: -508.3x - 30.4 = 0

Step 5: Move constant term to the other side: -508.3x = 30.4

Step 6: Solve for 'x': x = 30.4 / (-508.3) x ≈ -0.0597 (rounded to four decimal places)

So, the solution for this equation is approximately 'x = -0.0597'.