Question

3х(2х+3)=2х(х+4,5)+2

Answer 1

Ответ:

$x = \frac{1}{\sqrt{2} },$ $-\frac{1}{\sqrt{2} }$

Объяснение:

Раскроем скобки в левой и правой частях уравнения:

3x * 2x + 3 * 3x = 2x * x + 4,5 * 2x + 2

6x² + 9x = 2x² + 9x + 2

6x² - 2x² + 9x - 9x = 2

4x² = 2

x² = 1/2

$x = \frac{1}{\sqrt{2} }$               $x = -\frac{1}{\sqrt{2} }$

Answer 2

Let's solve the equation step by step:

1. Distribute the 3x on the left side of the equation:

   3x * 2x + 3 * 3x = 2x * (x + 4.5) + 2

   This simplifies to:

   6x^2 + 9x = 2x * (x + 4.5) + 2

2. Distribute the 2x on the right side of the equation:

   6x^2 + 9x = 2x^2 + 9x + 2

3. Now, let's move all terms to one side of the equation to set it to zero:

   6x^2 + 9x - 2x^2 - 9x - 2 = 0

4. Simplify the equation further:

   4x^2 - 2 = 0

5. Add 2 to both sides of the equation:

   4x^2 = 2

6. Divide both sides by 4:

   x^2 = 2/4

7. Simplify the right side:

   x^2 = 1/2

8. Take the square root of both sides:

   x = ±√(1/2)

So, the solutions for the equation are:

x = √(1/2) or x = -√(1/2)