(ix) 6m2 + m = 2
Sol. 6m2 + m = 2
Dividing both the sides by 6 we get,
m2 + m/6 = 1/3 ............(i)
Third term = ( ½ × coefficient of m)2
= ( ½ × 1/6)2
= (1/12)2
= 1/144
Adding 1/144 to both sides of (i) we get,
m2 + m/6 + 1/144 = 1/3 + 1/144
∴ (m + 1/12)2 = 49/144
∴ m + 1/12 = ±√(49/144)
∴ m + 1/12 = ± 7/12
∴ m = - 1/12 ± 7/12
∴ m = (-1 ± 7)/12
∴ m = (-1 + 7)/12 or (-1 - 7)/12
∴ m = 6/12 or -8/12
∴ m = ½ or – 2/3
