Question

Решить уравнение -6=(x-2)(x-2)-8x

Answer 1

Решение приложено снизу

Ответ : х = 5/6

Answer 2

To solve the equation -6 = (x-2)(x-2) - 8x, follow these steps:

Step 1: Expand the right side of the equation. Step 2: Simplify the equation by combining like terms. Step 3: Move all terms to one side to set the equation equal to zero. Step 4: Solve the resulting quadratic equation using factoring or the quadratic formula. Step 5: Check if the solutions obtained are valid for the original equation.

Let's proceed with the solution:

Step 1: Expand the right side of the equation. -6 = x^2 - 4x + 4 - 8x

Step 2: Simplify the equation by combining like terms. -6 = x^2 - 12x + 4

Step 3: Move all terms to one side to set the equation equal to zero. x^2 - 12x + 4 + 6 = 0

Step 4: Solve the quadratic equation. To solve the quadratic equation, you can use either factoring or the quadratic formula. In this case, we'll use the quadratic formula:

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

In the equation x^2 - 12x + 4 = 0, a = 1, b = -12, and c = 4.

x = [12 ± √((-12)^2 - 4 * 1 * 4)] / 2 * 1 x = [12 ± √(144 - 16)] / 2 x = [12 ± √128] / 2 x = [12 ± 8√2] / 2

Step 5: Simplify the solutions. x = (12 + 8√2) / 2 x = 6 + 4√2

x = (12 - 8√2) / 2 x = 6 - 4√2

So the solutions to the equation are: x = 6 + 4√2 x = 6 - 4√2