Question

Use the substitution y = 2x + 3 to solve for x, if` 4 (2x + 3)^2 − (2x + 3) − 14 = 0 `

Answer 1

4 (2x+3)^2 − (2x + 3) − 14 = 0
Put 2x + 3 = y
`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
Then 2x + 3 – 2 = 0 Or 4(2x + 3) + 7 = 0
⟹ 2x = – 1 Or 8x = – 19 

`⟹x=(-1)/2`       or `x=(-19)/8`