Question

$6 {x}^{2} - 7x + 2 = 0$
find the roots by completing the square method​

Answer 1

Let 6x2 – 7x + 2 = 0

⇒ 6x2 – 7x  = -2

⇒x2 – 7x/6 =  -2/6

Here b = -7/6

b/2 = -7/12

Adding both sides by (-7/12)²

x2 – 7x/6 =  -2/6

⇒x2 – 7x/6 +(-7/12)² =  -2/6 +(-7/12)²

⇒x2 – 7x/6 +(-7/12)² =  -2/6 +  49/144

(x - 7/12)² = -48/144 + 49/144

(x - 7/12)² = 1/144

x - 7/12 = √( 1/144 )

x - 7/12 =  ± 1/12

x = 1/12 + 7/12  or x = -1/12 + 7/12

x = 8/12 = 2/3 or x = 6/12 = 1/2

x = 2/3 or x = 1/2

Answer 2

Answer:

Roots are 2/3 and 1/2

Complete solution :-

Let 6x2 – 7x + 2 = 0

⇒ 6x2 – 7x  = -2

⇒x2 – 7x/6 =  -2/6

Here b = -7/6

b/2 = -7/12

Adding both sides by (-7/12)²

x2 – 7x/6 =  -2/6

⇒x2 – 7x/6 +(-7/12)² =  -2/6 +(-7/12)²

⇒x2 – 7x/6 +(-7/12)² =  -2/6 +  49/144

(x - 7/12)² = -48/144 + 49/144

(x - 7/12)² = 1/144

x - 7/12 = √( 1/144 )

x - 7/12 =  ± 1/12

x = 1/12 + 7/12  or x = -1/12 + 7/12

x = 8/12 = 2/3 or x = 6/12 = 1/2

x = 2/3 or x = 1/2