Question

( 7x+1 ) * ( 2-x ) = 8

Answer 1

$(7x+1)(2-x)=8\\14x-7x^2+2-x=8\\7x^2-13x+6=0\\x_{1,2}=\frac{13^+_-\sqrt{1}}{14}\\x_1=1\ ;x_2=\frac{6}{7}$

Answer 2

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

1. Expand the left side of the equation by multiplying the two binomials:

(7x + 1) * (2 - x) = 14x - 7x^2 + 2 - x = 14x - 7x^2 + 2 - x

2. Set the equation equal to 8:

14x - 7x^2 + 2 - x = 8

3. Rearrange the terms to form a quadratic equation in standard form (ax^2 + bx + c = 0):

-7x^2 + 14x - x + 2 - 8 = 0

4. Combine like terms:

-7x^2 + 13x - 6 = 0

5. Now, you have a quadratic equation. To solve it, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = -7, b = 13, and c = -6. Plug these values into the formula:

x = (-13 ± √(13² - 4(-7)(-6))) / (2(-7))

x = (-13 ± √(169 - 168)) / (-14)

x = (-13 ± √1) / (-14)

6. Now, simplify further:

x = (-13 ± 1) / (-14)

Now, you have two possible solutions:

a) x = (-13 + 1) / (-14) = (-12) / (-14) = 6/7

b) x = (-13 - 1) / (-14) = (-14) / (-14) = 1

So, the equation (7x + 1) * (2 - x) = 8 has two solutions: x = 6/7 and x = 1.