Question

3) (z - 6)(2 + 5) - (z - 2)2 =30;​

Answer 1

Ответ:

13.6

Объяснение:

2z+5z-12-30-2z+4=30

5z=68

z=13.6

Answer 2

Ответ:

(z-6)*(2+5)*(z-2)*2=30

(z-6)*7-(2z-4)=30

7z*42-2z+4=30

5z-38=30

5z=30+38

5z=68

z=68/5

Answer 3

Let's solve the given equation step by step:

1. Distribute the terms inside the parentheses: (z - 6)(2 + 5) - (z - 2)2 = 30

   (z - 6)(7) - (z - 2)2 = 30

2. Multiply the terms in parentheses: 7z - 42 - (z - 2)2 = 30

3. Expand the second set of parentheses: 7z - 42 - (z^2 - 4z + 4) = 30

4. Distribute the negative sign to all terms within the second set of parentheses: 7z - 42 - z^2 + 4z - 4 = 30

5. Combine like terms: (7z + 4z) - (z^2) - 42 - 4 + 30 = 0

6. Simplify further: 11z - z^2 - 16 = 0

7. Rearrange the equation to set it to zero: -z^2 + 11z - 16 = 0

Now, this equation is a quadratic equation in the form of ax^2 + bx + c = 0, where a = -1, b = 11, and c = -16.

To solve the quadratic equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values: z = (-(11) ± √((11)^2 - 4(-1)(-16))) / 2(-1)

Simplify further: z = (-11 ± √(121 - 64)) / -2 z = (-11 ± √57) / -2

Now, we have two solutions for z: z = (-11 + √57) / -2 ≈ -3.15 z = (-11 - √57) / -2 ≈ 14.15

So the solutions to the equation are approximately z = -3.15 and z = 14.15.