Question

o quadrado de um número é igual a seu dobro somado com 24. determine esse número

Answer 1

x² = 2x + 24 
x² - 2x - 24 = 0

a = 1
b = -2
c = -24

Δ = b² -4 .a . c
Δ = (-2)² -4 . 1 . (-24)
Δ = 4 + 96
Δ = 100

$\mathtt{\dfrac{-b+-~\sqrt{\Delta}}{2~.~a}~~=~~\dfrac{-(-2)+-~\sqrt{100}}{2~.~1}~~=~~\dfrac{2+-~10}{2}} \\ \\ \\ \mathtt{x' = \dfrac{2+10}{2}~~=~~\dfrac{12}{2}~~=~~6} \\ \\ \\ \mathtt{x'' =\dfrac{2-10}{2}~~=~~ -\dfrac{8}{2}~~=~~-4} \\ \\ \\ \boxed{\boxed{\mathtt{Resposta: -4~~~e ~~6}}}$