Question

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

Answer 1

Answer:

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

Step-by-step 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

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

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

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

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