Question

Solve each of the following equations by factorization: 

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

Answer 1

`9/2x=5+x^2`
⟹ `9x = 10 + 2x^2`
⟹ `2x^2 – 9x + 10 = 0`
⟹` 2x^2 – 5x – 4x + 10 = 0`
⟹ `x(2x – 5) –2(2x – 5) = 0`
⟹ `(2x – 5) (x – 2) = 0`
Since `2x – 5 = 0  "Or" x – 2 = 0`
Then ` x = 5/2  "Or"   x = 2`