Question

(2x+6)²+(x-6+1)(x+6-1)=6*6+4

Answer 1

Ответ:

х1= -$\frac{29}{5}$    

x2=1

Объяснение:

Answer 2

Let's simplify the given equation step by step:

(2x + 6)² + (x - 6 + 1)(x + 6 - 1) = 6 * 6 + 4

First, we can square the binomial term (2x + 6)²:

(4x² + 24x + 36) + (x - 6 + 1)(x + 6 - 1) = 36 + 4

Now, simplify the expressions within the parentheses:

(4x² + 24x + 36) + (x - 5)(x + 5) = 36 + 4

Next, multiply the two binomials (x - 5)(x + 5) using the difference of squares formula (a² - b² = (a + b)(a - b)):

(4x² + 24x + 36) + (x² - 25) = 36 + 4

Now, distribute the (x² - 25) term:

4x² + 24x + 36 + x² - 25 = 36 + 4

Combine like terms on both sides of the equation:

5x² + 24x + 11 = 40

Now, subtract 40 from both sides of the equation:

5x² + 24x + 11 - 40 = 0

5x² + 24x - 29 = 0

Now you have a quadratic equation in the form of ax² + bx + c = 0, where a = 5, b = 24, and c = -29. You can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values:

x = (-24 ± √(24² - 4 * 5 * (-29))) / (2 * 5)

x = (-24 ± √(576 + 580)) / 10

x = (-24 ± √1156) / 10

x = (-24 ± 34) / 10

Now, you have two possible solutions:

1. x = (-24 + 34) / 10 = 10 / 10 = 1
2. x = (-24 - 34) / 10 = -58 / 10 = -5.8

So, the solutions for the equation are x = 1 and x = -5.8.