Question

8(x - 6) + x(18 - x) = 2(x - 3)²

Answer 1

Ответ:

Пошаговое объяснение:

8(x - 6) + x(18 - x) = 2(x - 3)²

упрощаем выражение путем раскрытия скобок и возведение в квадрат

8х - 48 +18х -х² = 2х² - 12х +18

-3х² + 38х -66=0

$D=b^2-4ac=652\\\\x_1=\frac{19-\sqrt{163} }{3} \\\\x_2=\frac{19+\sqrt{163} }{3}$

Answer 2

Let's solve the equation step by step:

1. First, expand and simplify both sides of the equation:

   8(x - 6) + x(18 - x) = 2(x - 3)²

   8x - 48 + 18x - x² = 2(x - 3)²

2. Next, distribute the constants on both sides:

   8x + 18x - 48 - x² = 2(x - 3)²

   26x - 48 - x² = 2(x - 3)²

3. Expand the square on the right side by multiplying it by itself:

   26x - 48 - x² = 2(x² - 6x + 9)

4. Distribute the 2 on the right side:

   26x - 48 - x² = 2x² - 12x + 18

5. Now, move all the terms to one side of the equation to set it equal to zero:

   0 = 2x² - 12x + 18 - (26x - 48 - x²)

   0 = 2x² - 12x + 18 - 26x + 48 + x²

6. Combine like terms:

   0 = 2x² - x² - 12x - 26x + 18 + 48

   0 = x² - 38x + 66

7. Now, we have a quadratic equation in the form ax² + bx + c = 0, where a = 1, b = -38, and c = 66. To solve for x, we can use the quadratic formula:

   x = (-b ± √(b² - 4ac)) / (2a)

   x = (-(-38) ± √((-38)² - 4(1)(66))) / (2(1))

   x = (38 ± √(1444 - 264)) / 2

   x = (38 ± √1180) / 2

   x = (38 ± 2√295) / 2

8. Now, simplify the expression further:

   x = 19 ± √295

So, the solutions to the equation are:

x = 19 + √295 x = 19 - √295