ANSWER
[tex]x=1,x=3,x=6[/tex]
EXPLANATION
To solve an equation using the x-intercept method, we must graph the corresponding function and locate x-values of the x-intercepts.
The given polynomial equation is
[tex] {x}^{3} - 10 {x}^{2} + 27x - 18 = 0[/tex]
The graph of the corresponding function
[tex]y = {x}^{3} - 10 {x}^{2} + 27x - 18 [/tex]
Is shown in the attachment.
The x-intercepts are:(1,0), (3,0), (6,0)
Therefore the solutions are,
[tex]x=1,x=3,x=6 [/tex]
