1. **State the problem:** Find the solutions of the equation $$2 - x^2 = -x$$ by graphing. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero: $$2 - x^2 + x = 0$$ which simplifies to $$-x^2 + x + 2 = 0$$ 3. **Rewrite in standard quadratic form:** Multiply both sides by $$-1$$ to make the leading coefficient positive: $$x^2 - x - 2 = 0$$ 4. **Factor the quadratic:** Find two numbers that multiply to $$-2$$ and add to $$-1$$. These are $$-2$$ and $$1$$. $$x^2 - x - 2 = (x - 2)(x + 1) = 0$$ 5. **Solve for $$x$$:** Set each factor equal to zero: $$x - 2 = 0 \Rightarrow x = 2$$ $$x + 1 = 0 \Rightarrow x = -1$$ 6. **Interpretation:** The solutions are $$x = -1$$ or $$x = 2$$, which correspond to the points where the parabola $$y = 2 - x^2$$ intersects the line $$y = -x$$. **Final answer:** $$x = -1 \text{ or } x = 2$$