8х=х-х2

To solve the equation 8x = x - x^2, we'll bring all the terms to one side and set the equation equal to zero:

8x = x - x^2 0 = x - x^2 - 8x

Now, let's rearrange the terms:

0 = -x^2 - 8x + x

Combining like terms:

0 = -x^2 - 7x

To solve this quadratic equation, we'll attempt to factor it:

0 = x(-x - 7)

Now we can set each factor equal to zero and solve for x:

x = 0 -x - 7 = 0

For the second equation, we'll add 7 to both sides:

-x = 7

Then, multiply both sides by -1 to isolate x:

x = -7

Therefore, the solutions for the equation 8x = x - x^2 are x = 0 and x = -7.