Question

Solve equation using factorisation method:

`9/2 x = 5 + x^2`

Answer 1

`9/2 x = 5 + x^2` 

⇒ 9x = 10 + 2x²

⇒ 2x² – 9x + 10 = 0

⇒ 2x² – 5x – 4x + 10 = 0

⇒ x(2x – 5) – 2(2x – 5) = 0

⇒ (2x – 5)(x – 2) = 0

Since 2x – 5 = 0 or x – 2 = 0

∴ 2x – 5 = 0

∴  2x = 5

∴  x = `5/2`

∴  x – 2 = 0

∴  x = 2

Then x = `5/2` or x = 2