Answer:
x=6
Step-by-step explanation:
The equation ...
[tex]x^3-6x^2+3x-18=0[/tex]
can be factored by grouping to get a linear factor and a quadratic factor. The linear factor always has a real zero. This quadratic factor does not.
[tex]=(x^3-6x^2)+(3x-18)=x^2(x-6)+3(x-6)\\\\=(x-6)(x^2+3)=0[/tex]
The one real solution is x=6, the value of x that makes (x-6) = 0.
