Question

Решите: 1)2х-х²=0 2)(3х+1)(2х+6)=8(2х+3)

Answer 1

2х-х^2=0
х(2-х)=0
х=0 х=2

Answer 2

To solve the given equations, we'll start by simplifying and then finding the values of 'x' that satisfy each equation.

1. 2x - x² = 0

Step 1: Factor out common terms, which is 'x' in this case: x(2 - x) = 0

Step 2: Now, we set each factor to zero and solve for 'x': x = 0 (from the first factor: x = 0) 2 - x = 0 (from the second factor)

Step 3: Solve for 'x': 2 - x = 0 x = 2

So, the solutions for this equation are x = 0 and x = 2.

2. (3x + 1)(2x + 6) = 8(2x + 3)

Step 1: Expand the equation: 6x² + 18x + 2x + 6 = 16x + 24

Step 2: Combine like terms: 6x² + 20x + 6 = 16x + 24

Step 3: Move all terms to one side of the equation to set it to zero: 6x² + 20x + 6 - 16x - 24 = 0

Step 4: Simplify the equation: 6x² + 4x - 18 = 0

Step 5: Divide the entire equation by 2 to simplify it further: 3x² + 2x - 9 = 0

Now, you can use the quadratic formula to find the values of 'x', or you can try to factor the equation if possible. Let's use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / 2a

In our equation, a = 3, b = 2, and c = -9:

x = (-(2) ± √((2)² - 4 * 3 * (-9))) / 2 * 3 x = (-2 ± √(4 + 108)) / 6 x = (-2 ± √112) / 6 x = (-2 ± 4√7) / 6

Now, we have two possible solutions:

1. x = (-2 + 4√7) / 6
2. x = (-2 - 4√7) / 6

These are the solutions for the second equation.