The sum of a number and its square is 63/4, find the numbers.
Let the number be ‘a’
⇒ a + a2 = 63/4
⇒ 4a2 + 4a – 63 = 0
⇒ 4a2 + 18a – 14a – 63 = 0
⇒ 2a(2a + 9) – 7(2a + 9) = 0
⇒ (2a – 7)(2a + 9) = 0
⇒ a = 7/2 or – 9/2