2×2 – 7x + 3 = 0
Dividing both side by 2
x² – 7/2 x + 3/2 = 0 ⇒ x² – 7/2 x = – 3/2
Adding [1/2(7/2)]² on both the sides, we get
x² – 7/2 x + (7/4)² = – 3/2 + (7/4)² [(as x = -b±√(b²- 4ac)]/2a]
⇒ (x – 7/4)² = – 3/2 + 49/16 ⇒ (x – 7/4)² = – 24 + 49/16
⇒ (x – 7/4)² = 25/16
⇒ x – 7/4 = ± 5/4
Either x – 7/4 = 5/4 or x – 7/4 = – 5/4
⇒ x = 5/4 + 7/4 or x – 5/4 + 7/4
⇒ x = 5+7/4 = 12/4 = 3 x 5+7/4 = 2/4 = 1/2
Hence, the roots of the quadratic equation are 3 and 1/2.