Question

(x - 2)² + 8x = (x - 1)(1 + x)​

Answer 1

Ответ:

ответ можно ещё записать как x = –1,25

Answer 2

To solve the equation (x - 2)² + 8x = (x - 1)(1 + x), we'll start by expanding and simplifying both sides of the equation.

Expanding the left side: (x - 2)² + 8x = (x - 2)(x - 2) + 8x = x² - 4x + 4 + 8x

Expanding the right side: (x - 1)(1 + x) = x(1 + x) - 1(1 + x) = x² + x - 1 - x = x² - 1

Now, we have the equation: x² - 4x + 4 + 8x = x² - 1

Let's simplify and solve for x:

Rearranging the terms: x² - 4x + 8x - x² + 4 = -1

Combining like terms: 4x + 4 = -1

Moving the constant term to the right side: 4x = -1 - 4

Simplifying: 4x = -5

Dividing both sides by 4: x = -5/4

Therefore, the solution to the equation (x - 2)² + 8x = (x - 1)(1 + x) is x = -5/4.