Question

Решите уравнения. 1. -6х-х^2=9 2. 2+x^2=11x 3. -9-4x^+12x=0 4. 4+9x^2=0 5. 10x+25x^2=-1 6. x^2+2,3x=0 7. -15=-3x^2 8. -x^2=2+2x 9. 4+3x^2=-7x 10. 14-x-3x^2=0 11. x^2+25=10x 12. -8+18x-5x^2

Answer 1

В третьем не понятно..."x" в какой степени?

Answer 2

1. -6x - x^2 = 9

Rearranging and simplifying, we get:

x^2 + 6x + 9 = 0

This is a quadratic equation in standard form. We can solve for x by factoring:

(x + 3)^2 = 0

Taking the square root of both sides, we get:

x + 3 = 0

Therefore, the solution is:

x = -3

2. 2 + x^2 = 11x

Rearranging and simplifying, we get:

x^2 - 11x + 2 = 0

Using the quadratic formula:

x = (11 ± √(11^2 - 412)) / (2*1)

x = (11 ± √117) / 2

Therefore, the solutions are:

x ≈ 10.03 or x ≈ 0.97

3. -9 - 4x^2 + 12x = 0

Rearranging and simplifying, we get:

4x^2 - 12x - 9 = 0

Using the quadratic formula:

x = (12 ± √(12^2 - 44(-9))) / (2*4)

x = (3 ± √21) / 2

Therefore, the solutions are:

x ≈ 2.79 or x ≈ 0.21

4. 4 + 9x^2 = 0

This equation has no real solutions, since the square of any real number is non-negative.

5. 10x + 25x^2 = -1

Rearranging and simplifying, we get:

25x^2 + 10x + 1 = 0

Using the quadratic formula:

x = (-10 ± √(10^2 - 4251)) / (2*25)

x = (-10 ± √-240) / 50

Since the square root of a negative number is not real, this equation has no real solutions.

6. x^2 + 2.3x = 0

Factoring out x, we get:

x(x + 2.3) = 0

Therefore, the solutions are:

x = 0 or x = -2.3

7. -15 = -3x^2

Dividing both sides by -3, we get:

5 = x^2

Taking the square root of both sides, we get:

x = ±√5

Therefore, the solutions are:

x ≈ 2.24 or x ≈ -2.24

8. -x^2 = 2 + 2x

Rearranging and simplifying, we get:

x^2 + 2x + 2 = 0

Using the quadratic formula:

x = (-2 ± √(2^2 - 412)) / (2*1)

x = (-2 ± √-4) / 2

Since the square root of a negative number is not real, this equation has no real solutions.

9. 4 + 3x^2 = -7x

Rearranging and simplifying, we get:

3x^2 + 7x + 4 = 0

Using the quadratic formula:

x = (-7 ± √(7^2 - 434)) / (2*3)

x = (-7 ± √25) / 6

Therefore, the solutions are:

x = -1 or x ≈ -1