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

Completing the square method is one of the methods to find the roots of the given quadratic equation.

Given quadratic equation

3x2 – 5x + 2 = 0

Solution

The given equation is not in the form to apply the method of completing squares. The coefficient of x2 is not 1.

To make the coefficient 1, we need to divide the whole equation by 3.
x2 – 5/3 x + 2/3 = 0
Comparing with the standard form of the equation

Stand form of equation is

ax2 + bx + c = 0, where a,b and c are real numbers such that a ≠ 0 and x is a variable.
b = -5/3; c = ⅔
c – b2/4 = ⅔ – [(5/3)2/4] = ⅔ – 25/36 = -1/36
So,
= (x – 5/6)2 = 1/36
= (x – 5/6)= ± √(1/36)
= x – 5/6 = ±1/6
= x = 1, -2/3

Answer

Hence the roots of the equation are x = 1, -2/3

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