Question

2x^2=2(1-2x)+x Нужна помощь, пожалуйста

Answer 1

2x² = 2 * (1 - 2x) + x
2x² - x = 2 - 4x
2x² - x + 4x - 2 = 0
2x² +3x - 2 = 0
D= 9 - 4 * 2 * (-2) = 9 + 16 = 25
x1/2 = (-3 ± √25) / 2 * 2 = (-3 ± 5) / 4
x1 = -8 / 4 = -2
x2 = 2 / 4 = 0.5
Ответ: -2; 0,5

Answer 2

Solving the Equation 2x^2=2(1-2x)+x

To solve the equation 2x^2 = 2(1-2x) + x, we can follow these steps:

1. Rearrange the Equation: - Start by rearranging the equation to bring all terms to one side and set the equation to zero.

2. Apply the Quadratic Formula: - Once the equation is in the form ax^2 + bx + c = 0, we can apply the quadratic formula to find the solutions for x.

Let's proceed with these steps to solve the given equation.

Rearranging the Equation:

We rearrange the equation 2x^2 = 2(1-2x) + x to bring all terms to one side and set the equation to zero: - 2x^2 = 2 - 4x + x - 2x^2 = 2 - 3x

Applying the Quadratic Formula:

Now, we can apply the quadratic formula to find the solutions for x: - The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by: - x = (-b ± √(b^2 - 4ac)) / (2a)

By comparing the rearranged equation with the standard form ax^2 + bx + c = 0, we can identify a=2, b=-3, and c=-2. Substituting these values into the quadratic formula will give us the solutions for x.

Let's calculate the solutions for x using the quadratic formula.

Calculating the Solutions for x:

Using the quadratic formula: - x = (-(-3) ± √((-3)^2 - 4*2*(-2))) / (2*2) - x = (3 ± √(9 + 16)) / 4 - x = (3 ± √25) / 4 - x = (3 ± 5) / 4

So, the solutions for x are: - x = (3 + 5) / 4 = 8 / 4 = 2 - x = (3 - 5) / 4 = -2 / 4 = -0.5

Therefore, the solutions for the equation 2x^2 = 2(1-2x) + x are: - x = 2 - x = -0.5

These are the values of x that satisfy the given equation.