Question: Use your graphing calculator to solve the equation graphically for all real solutions $x^3 - 2.1x^2 - 21.16x + 8.736 = 0$ Solutions = Make sure your answers are accurate to at least two decimals Graph shape: a cubic polynomial curve for $y = x^3 - 2.1x^2 - 21.16x + 8.736$, with the graph positioned in the center.

1. **State the problem:** We need to find all real solutions to the cubic equation $$x^3 - 2.1x^2 - 21.16x + 8.736 = 0$$ by graphing the function $$y = x^3 - 2.1x^2 - 21.16x + 8.736$$ and identifying where it crosses the x-axis. 2. **Recall:** The real solutions to the equation correspond to the x-values where the graph of $$y$$ intersects the x-axis (i.e., where $$y=0$$). 3. **Graph the function:** Plot $$y = x^3 - 2.1x^2 - 21.16x + 8.736$$ using a graphing calculator or software. 4. **Identify approximate roots:** From the graph, estimate the x-values where the curve crosses the x-axis. These are the real roots. 5. **Refine roots:** Use the calculator's root-finding feature or zoom in on the graph to find roots accurate to at least two decimal places. 6. **Solutions found:** - First root approximately at $$x \approx -3.90$$ - Second root approximately at $$x \approx 0.42$$ - Third root approximately at $$x \approx 5.58$$ 7. **Final answer:** The real solutions to the equation $$x^3 - 2.1x^2 - 21.16x + 8.736 = 0$$ are approximately $$x = -3.90, 0.42, 5.58$$.