Question

Solve the following quadratic equations by factorization: 

`4(2x – 3)^2 – (2x – 3) – 14 = 0`

Answer 1

`4(2x – 3)^2 – (2x – 3) – 14 = 0`
Let `2x – 3 = y`
Then `4y^2 – y – 14 = 0`
⟹` 4y^2 – 8y + 7y – 14 = 0`
⟹` 4y^(y – 2) + 7 ( y – 2) = 0`
⟹ (y – 2) (4y + 7) = 0
If y – 2 = 0 Or 4y + 7 = 0
⟹y = 2 or y = `−7/4`
⟹ `2x – 3 = 2   "Or"   2x – 3 = − 7/4`
⟹` 2x = 5   "Or"   2x = 5/4`
⟹ `x = 5/2   "Or"    x = 5/8`