Question

7x^2=6-11х * 2 балла -7; 2/7 -2; 6/7 -2; 3 -2; 3/7

Answer 1

$7 {x}^{2} = 6 - 11x \\ 7 {x}^{2} + 11x - 6 = 0 \\ D = 11 {}^{2} - 4 \times ( - 6) \times 7 = 121 + 168 = 289 \: (17) \\ x_{1} = \frac{ - 11 + 17}{14} = \frac{6}{14} = \frac{3}{7} \\ x_{2} = \frac{ - 11 - 17}{14} = \frac{ - 28}{14} = - 2 \\ Ответ: - 2 \: ; \: \frac{3}{7}$

Answer 2

To solve the equation 7x^2 = 6 - 11x, we need to bring all terms to one side of the equation to get a quadratic equation in standard form (ax^2 + bx + c = 0).

Let's simplify the equation step by step:

7x^2 + 11x - 6 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's try factoring:

(7x - 2)(x + 3) = 0

Now we can set each factor equal to zero:

7x - 2 = 0 or x + 3 = 0

Solving these two equations, we get:

7x = 2 or x = -3

Dividing both sides by 7 in the first equation:

x = 2/7 or x = -3

So the solutions to the equation 7x^2 = 6 - 11x are x = 2/7 and x = -3.

Now, let's evaluate the given expressions:

1. For x = 2/7: 2/7 - 2 = 2/7 - 14/7 = -12/7

2. For x = -2: 2/7 - 2 = 2/7 - 14/7 = -12/7

3. For x = 6/7: 6/7 - 2 = 6/7 - 14/7 = -8/7

4. For x = 3: 3 - 2 = 1

5. For x = 3/7: 3/7 - 2 = 3/7 - 14/7 = -11/7

So the evaluations of the expressions are:

1. x = 2/7: -12/7
2. x = -2: -12/7
3. x = 6/7: -8/7
4. x = 3: 1
5. x = 3/7: -11/7