Question

Show all work to solve by factoring 3x^2 − x − 2 = 0.

Answer 1

The solutions are x=1 and x=-2/3

Explanation:

we have

`3x^(2)-x-2=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`3x^(2)-x=2`

Factor the leading coefficient

`3(x^(2)-(1/3)x)=2`

Complete the square. Remember to balance the equation by adding the same constants to each side

`3(x^(2)-(1/3)x+(1/36))=2+(1/12)`

`3(x^(2)-(1/3)x+(1/36))=25/12`

Rewrite as perfect squares

`3(x-(1/6))^(2)=25/12`

`(x-(1/6))^(2)=25/36`

square root both sides

`(x-(1/6))=(+/-)(5/6)`

`x=(1/6)(+/-)(5/6)`

`x=(1/6)(+)(5/6)=1`

`x=(1/6)(-)(5/6)=-2/3`