Final answer:
To solve the equation f(x) = -x² + 2x, set the equation equal to zero and solve for x. The solutions are x = 0 and x = 2.
Step-by-step explanation:
To solve the equation f(x) = -x² + 2x, we set the equation equal to zero and solve for x. Rearranging the equation gives us -x² + 2x = 0. To factor out an x, we rewrite the equation as x(-x + 2) = 0. This equation is now equal to zero when either x = 0 or -x + 2 = 0.
Solving -x + 2 = 0, we find x = 2. Therefore, the solutions to the equation f(x) = -x² + 2x are x = 0 and x = 2.