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

4y² – y – 14 = 0

⇒ 4y² – 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`