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Question

Solve 3x25x+2=0 by completing the square method.

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Solution

Given 3x25x+2=0

Here, the coefficient of x2 is 3 and it is not a perfect square.

Multiply the equation throughout by 3.

(3x25x+2=0)×39x215x+6=0

Now, half of the coefficient of x is 52.b=52 and b2=(52)2

So, 9x215x+(52)2(52)2+6=0,(3x)215x+(52)2=(52)26

(3x52)2=2546=14
(Taking square root on both the sides)

3x52=±12

3x52=±12 or 3x52=12

3x=12+52 3x=5212

3x=62=3 3x=42=2

x=1 x=23

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