Question

Solve for ‘x’ if (x + 2)² − 6 (x + 2) – 16 = 0 by using the substitution y = x + 2.

Answer 1

Given:

(x + 2)² − 6(x + 2) − 16 = 0

y = x + 2

 y² − 6y − 16 = 0

`y = (-(-6) +- sqrt((-6)^2 - 4(1) (-16)))/(2(1))`

`y = (6+-sqrt(36+64))/2`

`= (6+- sqrt100)/2`

`= (6+-10)/2`

`y = (6+10)/2 = 16/2 = 8`

`y = (6-10)/2 = -4/2 = -2`

Case 1: 

x + 2 = 8

⇒ x = 6

Case 2:

x + 2 = −2

⇒ x = −4

x = 6 or x = −4​