Answer:
See the attached graph from which we obtain x = 3 as the only solution for the given equation.
Step-by-step explanation:
Notice that the equation [tex]x^2-6x=-9[/tex] is the same equation as when y = 0 in the function [tex]y = x^2-6x+9[/tex], since when y=0 we have:
[tex]y = x^2-6x+9\\0 = x^2-6x+9\\-9=x^2-6x[/tex]
Then what we need to find is for which values of "x" in the graph of y = x^2-6x+9, the graph touches or crosses the x-axis (that is when y=0)
We graph the given function in the x-y coordinate system and find where it renders zero for "y" (see attached graph).
We see that there is only one point of contact with the x-axis at x = 3
