Final answer:
The quadratic equation is factorable as (x - 3)(x - 7) = 0, which means the solutions are x = 3 and x = 7. These solutions are the x-intercepts on the graph of the equation.
Step-by-step explanation:
To solve the equation 2 - 10x + 21 = 0 by graphing, we must first correct the equation by assuming there is a typo, and it should read x² - 10x + 21 = 0. We look to factor the quadratic equation or alternatively use the quadratic formula to find its roots. However, in this case, the quadratic factors nicely to (x - 3)(x - 7) = 0.
The solutions are x = 3 and x = 7. When graphing, these two values would be the x-intercepts of the parabola described by the quadratic equation. Since we have two distinct real solutions, these will be entered in increasing order.
We do not need to use the quadratic formula in this instance, but for reference, that formula is x = (-b ± √(b² - 4ac)) / (2a).
The final answer is: 3, 7 as these are the points where the graph of the quadratic equation crosses the x-axis. No further solutions are present, and thus we do not enter 'no real solution'.