Question

Solve:

(x² + 5x + 4)(x² + 5x + 6) = 120

Answer 1

(x² + 5x + 4)(x² + 5x + 6) = 120

Let x² + 5x = y

Then (y + 4)(y + 6) = 120

`=>` y² + 6y + 4y + 24 – 120 = 0

`=>` y² + 10y – 96 = 0

`=>` y² + 16y – 6y – 96 = 0

`=>` y(y + 16) – 6(y + 16) = 0

`=>` (y + 16)(y – 16) = 0

Then y = –16 or y = 6

`=>` x² + 5x + 16 = 0 or x² + 5x – 6 = 0

`=> x = (-5 +- sqrt((5)^2 - 4(1)(16)))/(2(1))` or `x^2 + 6x - x - 6 = 0`

`=> x = (-5 +- sqrt(-39))/2` or `x(x + 6) - 1(x + 6) = 0`

(reject) or (x + 6)(x – 1) = 0

Then x = – 6 and x = 1