`(x+5)\sqrt{x^2+9} = x^2 + 5x + 9`
`⇔ x^4 + 10x^3 + 34x^2 +90x + 225 = x^4 + 10x^3 + 43x^2 + 90x + 81`
`⇔ x^4 + 10x^3 + 90x = x^4 + 10x^3 + 43x^2 + 90x - 144`
`⇔ x^4 + 10x^3 + 90x - (x^4+10x^3+43x^2+ 90x) = -144`
`⇔ -9x = -144`
`⇔ x^2 = 16`
`⇔ x = \pm4`
Vậy `S = {\pm4}`