Question

(2x+5)(x-6)+2(3x-2)=5(2x+1)²+11

Answer 1

Решение смотри на фото

Answer 2

To solve the given equation, let's simplify and solve step by step:

Given equation:

(2x+5)(x-6) + 2(3x-2) = 5(2x+1)² + 11

Let's start by expanding the expressions:

(2x+5)(x-6) = 2x(x) + 2x(-6) + 5(x) + 5(-6) = 2x² - 12x + 5x - 30 = 2x² - 7x - 30

2(3x-2) = 2 * 3x - 2 * 2 = 6x - 4

5(2x+1)² = 5 * (2x+1)^2 = 5 * (4x² + 4x + 1) = 20x² + 20x + 5

Now let's substitute these expanded expressions back into the original equation:

2x² - 7x - 30 + 6x - 4 = 20x² + 20x + 5 + 11

Simplify the equation:

2x² - 7x - 30 + 6x - 4 = 20x² + 20x + 16

Combine like terms:

2x² - x - 34 = 20x² + 20x + 16

Subtract 2x² and 20x² from both sides of the equation:

-19x² - x - 34 = 20x + 16

Add x to both sides:

-19x² - 34 = 21x + 16

Subtract 16 from both sides:

-19x² - 50 = 21x

Now, we have a quadratic equation. Let's bring all terms to one side:

-19x² - 21x - 50 = 0

At this point, we can either factor this quadratic equation or use the quadratic formula to solve for x. Let's use the quadratic formula:

The quadratic formula states that for an equation ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / 2a

For our equation, a = -19, b = -21, and c = -50:

x = (21 ± √((-21)² - 4*(-19)(-50))) / (2(-19))

Simplify under the square root:

x = (21 ± √(441 - 3800)) / (-38)

Since the value inside the square root is negative, the solutions will be complex.

x = (21 ± √(-3359)) / (-38)

x = (21 ± i√3359) / (-38)

So, the solutions for the equation are complex numbers:

x = (21 + i√3359) / -38 and x = (21 - i√3359) / -38.