Question

X(x+9)+(x+9)=0
Como posso resolver?

Answer 1

Deve aplicar a distributiva :

x(x+9) + (x + 9) = 0
x² + 9x + x + 9 = 0 
x² + 10x + 9 = 0       "se a pergunta pedir só fatoração, esse é a resposta"

a = 1
b = 10
c = 9

Δ = b² -4 .a . c
Δ = 10² -4 . 1 . 9
Δ = 100 - 36
Δ = 64

$\mathtt{\dfrac{-b+-~\sqrt{\Delta}}{2~.~a }~~=~~\dfrac{-10+-~\sqrt{64}}{2~.~1}~~=~~\dfrac{-10+-~8}{2}} \\ \\ \\ \mathtt{x' = \dfrac{-10+8}{2}~~=~~-\dfrac{2}{2}~~=~~-1} \\ \\ \\ \mathtt{x'' = \dfrac{-10-8}{2}~~=~~-\dfrac{18}{2}~~=~~-9}$

Resposta: S{-9  e  -1}