Question

(2х+5)(х-6)+2(3х+2)(3х-2=5(2х+1)²+11 уравнение

Answer 1

Раскрываем скобки, и формулы сокращенного умножения.

(2х+5)(х-6)+2(3х+2)(3х-2)=5(2х+1)^2+11

2х^2-12x+5x-30+2(9x^2-4)=5(4x^2+4x+1)+11

-7x-30-8=20х+16

-38-16=20х+7х

-54=27х

х=-54/27

х=-2,7

Answer 2

To solve the equation, we'll start by simplifying both sides and then proceed to solve for the variable "x."

Given equation: (2x+5)(x-6) + 2(3x+2)(3x-2) = 5(2x+1)² + 11

Step 1: Expand each side of the equation. On the left-hand side: (2x+5)(x-6) = 2x(x-6) + 5(x-6) = 2x^2 - 12x + 5x - 30 = 2x^2 - 7x - 30 Similarly, 2(3x+2)(3x-2) = 2(9x^2 - 4) = 18x^2 - 8

On the right-hand side: 5(2x+1)² = 5(4x^2 + 4x + 1) = 20x^2 + 20x + 5

Step 2: Now the equation becomes: 2x^2 - 7x - 30 + 18x^2 - 8 = 20x^2 + 20x + 5 + 11

Step 3: Combine like terms on each side of the equation: 20x^2 - 7x - 38 = 20x^2 + 20x + 16

Step 4: Move all terms to one side of the equation to set it equal to zero: 20x^2 - 20x^2 - 7x - 20x - 38 - 16 = 0

Step 5: Simplify further: -27x - 54 = 0

Step 6: Solve for "x": Subtract 54 from both sides: -27x = 54

Finally, divide by -27 to isolate "x": x = 54 / -27

x = -2

Therefore, the solution to the equation is x = -2.