Question

The product of a number and the number increased by 3 is 54. Find the two possible values the number could be.

Answer 1

$\large{\rm{\underline{\underline{Answer:}}}}$

Let the number be x.

Then, the number increased by 3 will be x + 3.

According to question,

x(x + 3) = 54

x² + 3x = 54

x² + 3x - 54 = 0

By middle term factorisation,

x² + 9x - 6x - 54 = 0

x(x + 9) - 6(x + 9) = 0

(x + 9)(x - 6) = 0

Equating to zeroes and we get,

x + 9 = 0

x = -9 (First value)

and,

x - 6 = 0

x = 6 (second value)