Question

Solve the following equation by factorisation method:

42 − x² = 3x − 2x

Answer 1

Given:

42 − x² = 3x − 2x

Simplify the RHS

3x − 2x = x

42 − x² = x

−x² − x + 42 = 0

x² + x − 42 = 0

Factorise

Find two numbers whose product = −42 and sum = 1.

These numbers are 7 and −6.

(x + 7) (x − 6) = 0

x + 7 = 0

⇒ x = −7

x − 6 = 0

⇒ x = 6

x = −7 or x = 6​