Question

X(3x-13,5)+4(3x-13,5)=0

Answer 1

Ответ:

3x^2-13.5x+12x-54=0

3x^2-1.5x-54=0

2x^2-x-36=0

D=289

X1=(1+17)/4=4.5

X2=(1-17)/4=-4

Answer 2

Let's solve the given equation:

X(3x - 13.5) + 4(3x - 13.5) = 0

First, distribute the X and 4 to the terms inside the parentheses:

3xX - 13.5X + 12x - 54 + 0 = 0

Now, combine like terms:

3x^2 - 13.5X + 12x - 54 = 0

To simplify the equation further, let's multiply all terms by 2 to get rid of the decimals:

6x^2 - 27X + 24x - 108 = 0

Combining like terms again:

6x^2 + 24x - 27x - 108 = 0

6x^2 - 3x - 108 = 0

Next, let's solve this quadratic equation. We can either factor it or use the quadratic formula. Since factoring might not be straightforward in this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 6, b = -3, and c = -108.

x = (-(-3) ± √((-3)^2 - 4 * 6 * -108)) / (2 * 6)

Simplifying further:

x = (3 ± √(9 + 2592)) / 12

x = (3 ± √(2601)) / 12

x = (3 ± 51) / 12

This gives us two possible solutions:

x₁ = (3 + 51) / 12 = 54 / 12 = 4.5

x₂ = (3 - 51) / 12 = -48 / 12 = -4

Therefore, the solutions to the equation are x = 4.5 and x = -4.