Question

0,4x+2×0,45×0,16x+6=x

Answer 1

4х+2*0.45*0.16Х+=Х
4Х+0.144Х+6=Х
4.144Х+6=Х
4.144Х-Х=-6
3.144Х=-6
х=-6÷3.144
х=-6÷3144/1000
х=-6×1000/3144
х=6×125/393
х=-2×125/131
х=-250/131

Answer 2

To solve the equation 0.4x + 2 × 0.45 × 0.16x + 6 = x, we can follow these steps:

1. Distribute the multiplication: 0.4x + 0.144x^2 + 6 = x

2. Move all the terms to one side of the equation to get a quadratic equation in standard form: 0.144x^2 + 0.4x - x + 6 = 0 0.144x^2 - 0.6x + 6 = 0

3. Multiply the entire equation by 100 to remove the decimal places: 144x^2 - 600x + 600 = 0

4. Simplify the equation by dividing all terms by their greatest common divisor (GCD), which is 12: 12(12x^2 - 50x + 50) = 0

5. Divide the equation by 12: 12x^2 - 50x + 50 = 0

Now, you can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 12, b = -50, and c = 50. Substituting these values into the formula:

x = (-(-50) ± √((-50)^2 - 4(12)(50))) / (2(12)) x = (50 ± √(2500 - 2400)) / 24 x = (50 ± √100) / 24 x = (50 ± 10) / 24

This gives us two possible solutions:

1. x = (50 + 10) / 24 x = 60 / 24 x = 2.5

2. x = (50 - 10) / 24 x = 40 / 24 x = 5/3 or approximately 1.67

Therefore, the solutions to the equation are x = 2.5 and x = 5/3 (or approximately 1.67).