Question

(2х-3)в квадраті -4х(х-2)=5

Answer 1

Ответ:

x=1……………..........………........……

Answer 2

To solve the equation "(2x-3)^2 - 4x(x-2) = 5", let's start by expanding the square and simplifying the expression:

(2x - 3)^2 - 4x(x - 2) = 5

Expanding the square:

(2x - 3)(2x - 3) - 4x(x - 2) = 5

Using the FOIL method to multiply the binomials:

(4x^2 - 6x - 6x + 9) - 4x(x - 2) = 5

Simplifying inside the parentheses:

(4x^2 - 12x + 9) - 4x(x - 2) = 5

Expanding the second term:

4x^2 - 12x + 9 - 4x^2 + 8x = 5

Simplifying further:

-4x^2 - 4x + 9 + 8x = 5

Combining like terms:

-4x^2 + 4x + 9 = 5

Now, let's rearrange the equation to set it equal to zero:

-4x^2 + 4x + 9 - 5 = 0

-4x^2 + 4x + 4 = 0

Dividing the equation by -4 to simplify the coefficients:

x^2 - x - 1 = 0

Now, we have a quadratic equation in the standard form ax^2 + bx + c = 0, where a = 1, b = -1, and c = -1.

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

x = (1 ± √((-1)^2 - 4(1)(-1))) / (2(1))

Simplifying:

x = (1 ± √(1 + 4)) / 2

x = (1 ± √5) / 2

Therefore, the solutions to the equation "(2x-3)^2 - 4x(x-2) = 5" are:

x = (1 + √5) / 2 x = (1 - √5) / 2