Question

2(x-4(x+5)x-4(2x-x^2)=0

Answer 1

Х - 4х -20 - 8х +4х² = 0
4х²-11х -20 = 0
D = 441
х₁ = (11 +21)/8 = 32/8 = 4
х₂ = (11 - 21)/8 = -10/8 = -5/4 = -1,25

Answer 2

To simplify the given expression, let's start by applying the distributive property to remove the parentheses:

2(x - 4(x + 5)x - 4(2x - x^2)) = 0

Now, let's simplify each term step by step:

1. Distribute the 4 in the second term: 2(x - 4x - 20x - 4(2x - x^2)) = 0 2(x - 4x - 20x - 8x + 4x^2) = 0

2. Combine like terms: 2(-23x - 8x + 4x^2) = 0 2(-31x + 4x^2) = 0

3. Multiply through by 1/2 to simplify the expression: -31x + 4x^2 = 0

Now, we have the quadratic equation:

4x^2 - 31x = 0

To solve this equation, we can factor out the common factor of x:

x(4x - 31) = 0

This equation is satisfied when either x = 0 or 4x - 31 = 0.

1. For x = 0, the equation is satisfied.

2. For 4x - 31 = 0, we can solve for x:

4x = 31 x = 31/4

Therefore, the solutions to the equation 2(x - 4(x + 5)x - 4(2x - x^2)) = 0 are x = 0 and x = 31/4.