Find the roots of the following quadratic equations, if they exist, by the method of completing the square: 2x² + x – 4 = 0

2x² + x – 4 = 0
Diving both sides by 2
x²+ 1/2 x – 2 = 0
⇒ x² + 1/2 x = 2
Adding [1/2(1/2)]² on both the sides, we get
x² + 1/2 x + (1/4)² = 2 + (1/4)² [As x = (-b±√(b²-4ac))/2a]
⇒ (x + 1/4)² = 2 + 1/16 ⇒ (x + 1/4)² = 32 + 1/16
⇒ (x + 1/4)² = 33/16 ⇒ x + 1/4 = ±√33/4
Either x + 1/4 = √33/4 or x + 1/4 = – √33/4
⇒ x = √33/4 – 1/4 or x = – √33/4 – 1/4
⇒ x = √33-1/4 or x = -√33-1/4
Hence, the roots of the quadratic equation are √33-1/4 and -√33-1/4.