Let's rewrite the given equation as a system of equations by treating each side of the equation as a separate function. The solutions to the original equation will be x-values of each point of intersection of the separated functions.
- x^2-x+6 = x^2-6x
⇕
y=- x^2-x+6 y=x^2-6x
To find these points, we will graph the functions using a graphing calculator. To do that we should enter them in the calculator by pushing Y= and writing their rules in the first two rows.
Next, by pushing GRAPH, the calculator will draw the graphs. Also, we can change the scale of the x-axis to decrease by 2 and the y-axis to increase by 2. We can do this by pushing WINDOW.
Now we are able to see that the graphs intersect at two points. Their x-coordinates can be found by pressing 2ND and then CALC.
After selecting the "intersect" option, we need to choose left and right boundaries for one of the points. Finally, the calculator asks for a guess where the intersection point might be. After that, it will calculate the exact point for us. We will have to do this twice, once for each point.
This equation's solutions are x≈ -0.886 and x≈3.386.
