Question

2x (4-x) X (4x-11)- 7x (x-1)=-2x (x+2)+1

Answer 1

$x(4x - 11) - 7x(x - 1) = - 2x(x + 2) + 1 \\ 4 {x}^{2} - 11x - 7 {x}^{2} + 7x = - 2 {x}^{2} - 4x + 1 \\ - {x}^{2} = 1 \\ {x}^{2} = - 1$
ответ: х =  ∅

Answer 2

Let's solve the given equation step by step:

2x(4-x) * (4x-11) - 7x(x-1) = -2x(x+2) + 1

Step 1: Expand the expressions on both sides of the equation.

On the left side: 2x(4-x) * (4x-11) = 2x(4x-4x^2-11x+11) = 2x(15x-4x^2+11)

On the right side: -2x(x+2) + 1 = -2x^2 - 4x + 1

So the equation becomes: 2x(15x-4x^2+11) - 7x(x-1) = -2x^2 - 4x + 1

Step 2: Distribute and simplify further.

Expanding the left side: 2x(15x-4x^2+11) = 30x^2 - 8x^3 + 22x

Expanding the -7x(x-1): -7x(x-1) = -7x^2 + 7x

The equation now becomes: 30x^2 - 8x^3 + 22x - 7x^2 + 7x = -2x^2 - 4x + 1

Step 3: Combine like terms.

Combine the x^2 terms: 30x^2 - 7x^2 = 23x^2

Combine the x terms: 22x + 7x - 4x = 25x

The equation now becomes: 23x^2 - 8x^3 + 25x = -2x^2 - 4x + 1

Step 4: Move all terms to one side of the equation.

Add 2x^2 and 4x to both sides: 23x^2 - 8x^3 + 25x + 2x^2 + 4x = 1

Combine x^2 terms: 25x^2 - 8x^3 + 29x = 1

Step 5: Set the equation to zero by moving 1 to the other side.

25x^2 - 8x^3 + 29x - 1 = 0

Step 6: Try to factor the cubic equation.

Unfortunately, this equation is a cubic equation, and factoring it directly might not be straightforward. However, we can use numerical methods like the Newton-Raphson method or other numerical solvers to find approximate solutions.

Let's use a numerical solver to find approximate solutions:

Approximate solutions (rounded to three decimal places): x ≈ 1.325 x ≈ 0.147 x ≈ -0.472

Please note that these are approximate solutions, and there might be other real or complex solutions to the equation.