Question

(2x-3)2-3(x-2)(x+2)=(x-2)(x+1)

Answer 1

Ответ: x1 = -0,921165, x2 = 2,17116

Объяснение:

Answer 2

Let's solve the given equation step by step:

$(2x - 3) \times 2 - 3(x - 2)(x + 2) = (x - 2)(x + 1)$

First, distribute and simplify on both sides:

$4x - 6 - 3(x^2 - 4) = x^2 - x - 2$

Now distribute the $-3$ inside the parentheses:

$4x - 6 - 3x^2 + 12 = x^2 - x - 2$

Combine like terms:

$-3x^2 + 4x + 6 = x^2 - x - 2$

Now move all terms to one side to set the equation to zero:

$-3x^2 + 4x + 6 - x^2 + x + 2 = 0$

Combine like terms again:

$-4x^2 + 5x + 8 = 0$

Now, we have a quadratic equation in the form $ax^2 + bx + c = 0$. Let's solve this quadratic equation using the quadratic formula:

The quadratic formula is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$.

In our equation, $a = -4$, $b = 5$, and $c = 8$.

Plugging these values into the quadratic formula:

$x = \frac{{-5 \pm \sqrt{{5^2 - 4 \times -4 \times 8}}}}{{2 \times -4}}$

$x = \frac{{-5 \pm \sqrt{{25 + 128}}}}{{-8}}$

$x = \frac{{-5 \pm \sqrt{{153}}}}{{-8}}$

Now, we'll calculate the values for $x$:

$x_1 = \frac{{-5 + \sqrt{{153}}}}{{-8}}$

$x_2 = \frac{{-5 - \sqrt{{153}}}}{{-8}}$

These are the solutions for the given equation.