Solve by completing the square

3x2 + x - 2 = 0

x = 2/3 or x = - 1

Step-by-step explanation by completing the square:

Solve for x:

3 x^2 + x - 2 = 0

Divide both sides by 3:

x^2 + x/3 - 2/3 = 0

Add 2/3 to both sides:

x^2 + x/3 = 2/3

Add 1/36 to both sides:

x^2 + x/3 + 1/36 = 25/36

Write the left hand side as a square:

(x + 1/6) ^2 = 25/36

Take the square root of both sides:

x + 1/6 = 5/6 or x + 1/6 = - 5/6

Subtract 1/6 from both sides:

x = 2/3 or x + 1/6 = - 5/6

Subtract 1/6 from both sides:

Answer: x = 2/3 or x = - 1