1. **State the problem:** Find the solutions of the equation $$2 - x^2 = -x$$ by graphing. 2. **Rewrite the equation:** To find the solutions, we want to find the values of $x$ where the parabola $$y = 2 - x^2$$ intersects the line $$y = -x$$. 3. **Set the equations equal:** Since both equal $y$, set them equal to each other: $$2 - x^2 = -x$$ 4. **Bring all terms to one side:** $$2 - x^2 + x = 0$$ 5. **Rewrite in standard quadratic form:** $$-x^2 + x + 2 = 0$$ Multiply both sides by $-1$ to simplify: $$\cancel{-}x^2 + \cancel{x} + \cancel{2} = \cancel{0} \implies x^2 - x - 2 = 0$$ 6. **Factor the quadratic:** $$x^2 - x - 2 = (x - 2)(x + 1) = 0$$ 7. **Solve for $x$:** Set each factor equal to zero: $$x - 2 = 0 \implies x = 2$$ $$x + 1 = 0 \implies x = -1$$ 8. **Interpretation:** The solutions to the equation are $$x = 2$$ and $$x = -1$$, which correspond to the points where the parabola and the line intersect on the graph. **Final answer:** $$x = 2 \text{ or } x = -1$$