Question

После каникул забыла как решаются такие уравнения (7x+1)(2-x)=8 помогите пожалуйста с решением(

Answer 1

(7x+1)(2-x)=8 7x*2-7x^2=8 -7x^2+14x-8=0 D=14^2-4*-7*-8=196-224=-28 нет корней

Answer 2

Solving the Equation (7x+1)(2-x)=8

To solve the equation *(7x+1)(2-x)=8*, we can follow these steps:

1. Expand the equation. 2. Simplify the equation. 3. Solve for *x*.

Let's go through each step.

Step 1: Expand the Equation

First, we expand the equation *(7x+1)(2-x)*.

Expanding *(7x+1)(2-x)* gives us: *(7x+1)(2-x) = 8* *14x - 7x^2 + 2 - x = 8*

Step 2: Simplify the Equation

Next, we simplify the equation by combining like terms.

The equation becomes: *-7x^2 + 13x - 6 = 0*

Step 3: Solve for x

Finally, we solve the quadratic equation *-7x^2 + 13x - 6 = 0* to find the values of *x*.

Using the quadratic formula: *x = (-b ± √(b^2 - 4ac)) / (2a)*

Where *a = -7*, *b = 13*, and *c = -6*.

Plugging these values into the quadratic formula, we get: *x = (-(13) ± √((13)^2 - 4(-7)(-6))) / (2(-7))* *x = (-(13) ± √(169 - 168)) / (-14)* *x = (-(13) ± √1) / (-14)* *x = (-(13) ± 1) / (-14)*

So, the solutions for *x* are: x = (-(13) + 1) / (-14) = -1 x = (-(13) - 1) / (-14) = 6/7

Therefore, the solutions to the equation *(7x+1)(2-x)=8* are x = -1 and x = 6/7.

I hope this helps! If you have any further questions, feel free to ask.