Answer:
The solutions are x=1 and x=-2/3
Step-by-step explanation:
we have
[tex]3x^{2}-x-2=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]3x^{2}-x=2[/tex]
Factor the leading coefficient
[tex]3(x^{2}-(1/3)x)=2[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]3(x^{2}-(1/3)x+(1/36))=2+(1/12)[/tex]
[tex]3(x^{2}-(1/3)x+(1/36))=25/12[/tex]
Rewrite as perfect squares
[tex]3(x-(1/6))^{2}=25/12[/tex]
[tex](x-(1/6))^{2}=25/36[/tex]
square root both sides
[tex](x-(1/6))=(+/-)(5/6)[/tex]
[tex]x=(1/6)(+/-)(5/6)[/tex]
[tex]x=(1/6)(+)(5/6)=1[/tex]
[tex]x=(1/6)(-)(5/6)=-2/3[/tex]
