Question

1)3x^2-6x=02)5x-10x^2=03)25x^2-15x=04)x^2-10x+25=05)x^2-81=0это всё уравнения решите без больших пропусков маленькие можно

Answer 1

$1) \: 3 {x}^{2} - 6x = 0 \\ 3x(x - 2) = 0$
Произведение равно нулю только тогда, когда хотя бы один из множителей равен нулю

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$2) \: 5x - 10 {x}^{2} = 0 \\ 5x(1 - 2x) = 0 \\ \\ 5x = 0 \\ x1 = 0 \\ \\ 1 - 2x = 0 \\ 2x = 1 \\ x2 = 0.5$

$3) \: 25 {x}^{2} - 15x = 0 \\ 5x(5x - 3) = 0 \\ \\ 5x = 0 \\ x1 = 0 \\ \\ 5x - 3 = 0 \\ 5x = 3 \\ x2 = 0.6$

$4) \: {x}^{2} - 10x + 25 = 0 \\ {(x - 5)}^{2} = 0 \\ x - 5 = 0 \\ x = 5$

$5) \: {x}^{2} - 81 = 0 \\ {x}^{2} = 81 \\ x1 = - 9 \\ x2 = 9$

Answer 2

1) 3x^2 - 6x = 0:

To solve this equation, we can factor out the common term of x: x(3x - 6) = 0

Setting each factor equal to zero, we have: x = 0 or 3x - 6 = 0

Solving the second equation for x: 3x = 6 x = 2

Therefore, the solutions to the equation 3x^2 - 6x = 0 are x = 0 and x = 2.

2) 5x - 10x^2 = 0:

Let's factor out the common term of x: x(5 - 10x) = 0

Setting each factor equal to zero, we have: x = 0 or 5 - 10x = 0

Solving the second equation for x: 10x = 5 x = 0.5

Therefore, the solutions to the equation 5x - 10x^2 = 0 are x = 0 and x = 0.5.

3) 25x^2 - 15x = 0:

We can factor out the common term of 5x: 5x(5x - 3) = 0

Setting each factor equal to zero, we have: 5x = 0 or 5x - 3 = 0

Solving the second equation for x: 5x = 3 x = 0.6

Therefore, the solutions to the equation 25x^2 - 15x = 0 are x = 0 and x = 0.6.

4) x^2 - 10x + 25 = 0:

This equation can be factored as a perfect square trinomial: (x - 5)^2 = 0

Setting the expression inside the parentheses equal to zero, we have: x - 5 = 0

Solving for x: x = 5

Therefore, the solution to the equation x^2 - 10x + 25 = 0 is x = 5.

5) x^2 - 81 = 0:

This equation is a quadratic equation in standard form. To solve it, we can use the square root property: x^2 = 81

Taking the square root of both sides, we have: x = ±√81

x = ±9

Therefore, the solutions to the equation x^2 - 81 = 0 are x = -9 and x = 9.

I hope this helps! Let me know if you have any further questions.