How do you solve using the completing the square method 3x2−4x−2=0?

1 Answer
Shwetank Mauria
Aug 6, 2016

x=−2−√103 or x=−2+√103

Explanation:

Let us divide each term of 3x2−4x−2=0 by 3, we get

x2−43x−23=0

Now recalling the identity (x−a)2=x2−2ax+a2 and comparing it with x2−43x, we need to add and subtract (43×2)2 to complete square. Hence x2−43x−23=0 is

⇔x2−2×46x+(46)2−(46)2−23=0 or

(x+46)2−(23)2−23=0 or

(x+23)2−49−69=0 or

(x+23)2−109=0 or

(x+23)2−(√103)2=0 or

(x+23+√103)(x+23−√103)=0

Hence, x+23+√103=0 or x+23−√103=0

i.e. x=−2−√103 or x=−2+√103

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