Question

Solve for ‘x’ if 3(2x + 3)² + 7 (2x + 3) − 40 = 0 by using the substitution y = 2x + 3.

Answer 1

Given:

3(2x + 3)² + 7 (2x + 3) − 40 = 0

Use substitution:

y = 2x + 3

3y² + 7y − 40 = 0

Two numbers that multiply to 3 × (−40) = −120 and add to 7:

Numbers are 15 and −8

3y² + 15y − 8y − 40 = 0

⇒ 3y(y + 5) − 8(y + 5) = 0

⇒ (3y − 8) (y + 5) = 0

Find values of y

3y − 8 = 0

⇒ y = `8/3`

y + 5 = 0

⇒ y = −5

Case 1:

2x + 3 = `8/3`

`2x = 8/3 - 3`

`= (8-9)/3`

`= (-1)/3`

⇒ x = `(-1)/6`

Case 2:

2x + 3 = −5

2x = −8

⇒ x = −4