6m2 + m = 2

(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