Solve the equation 3x² - 5 x + 2 = 0 by completing the square method.

The method of completing the square is one of the methods to solve quadratic equations by changing their form.

Answer: The value of x is 1 or 2/3 for the equation 3x² - 5 x + 2 = 0

Let's solve step by step.

Explanation:

3x² -5x +2 =0

Divide the quadratic equation with the coefficient of x² , that is 3,

⇒ x² -  (5x / 3) + (2 / 3) = 0

Divide the coefficient of x by 2, and square it (5 / 6)²

Now add it and subtract it in the equation,

⇒ x² - 5x / 3 + 2/ 3 + (5 / 6)² - (5 / 6)² = 0

⇒ x² - 5x / 3 + 2/ 3 + 25 / 36 - 25 / 36 = 0

⇒ x² - 5x / 3 + (24 - 25) / 36 + 25 / 36 = 0

⇒ x² - 5x / 3 + 25 / 36 = 1 / 36

⇒ (x - 5 / 6)² = (1 / 6)²

⇒ x - 5 / 6 = +- 1/6

x - 5 / 6 = 1 / 6 ----(1)      (or)  x - 5 / 6 = - 1 / 6 ----(2)

By solving the above equation (1) and (2), we get,

⇒ x = 1 or x = 4 / 6 

⇒ x = 1 or x = 2 / 3

Thus, the value of x is 1 or 2/3 for the equation 3x² - 5 x + 2 = 0