Now consider the equation 3x
2
– 5x + 2 = 0. Note that the coefficient of x
2
is not 1. So
we divide the entire equation by 3 so that the coefficient of x
2
is 1
∴ x²-5/3x+2/3=0
x²-5/3x=-2/3
x²-2.x.5/6=-2/3
x²-2.x.5/6+(5/6)²=-2/3+(5/6)²
[add (5/6)² both sides]
[x - 5/6] ^ 2 = - 2/3 + 25/36
(x - 5) ^ 2 =(12x-2)+(25x1)/36
(x - 5/6) =-24+25/ 36
(x - 5/6) ^ 2 = 1/36
(take square root both sides)
x - 5/6 = plus/minus 1/6
So, x=5/6 + 1/6 or x = 5/6 - 1/6
There fore, α=108 x = 4/6
i.e., x = 1 or x = 2/3
Therefore, the roots of the given equation are 1 and 2/3.
From the above examples we can deduce the following algorithm for completing the square.
Algorithm : Let the quadratic equation be ax
2
+ bx + c = 0 (a ¹ 0)