Question

em número ao quadrado mais o dobro desse número é igual a 35. Calcule esse número?

Answer 1

x² + 2x = 35
x² + 2x - 35 = 0

a = 1
b = 2
c = -35

Δ = b² -4 .a . c
Δ = 2² -4 . 1 . (-35)
Δ = 4 + 140
Δ = 144

$\mathtt{\dfrac{-b+-~\sqrt{\Delta}}{2~.~a}~~=~~\dfrac{-2+-~\sqrt{144}}{2~.~1}~~=~~\dfrac{-2+-~12}{2}} \\ \\ \\ \mathtt{x' = \dfrac{-2+12}{2}~~=~~\dfrac{10}{2}~~=~~ \boxed{5}} \\ \\ \\ \mathtt{x'' = \dfrac{-2-12}{2}~~=~~-\dfrac{14}{2}~~=~~\boxed{-7}}$


Resposta: S{-7 e 5}

Answer 2

$\\ x {}^{2} + 2x = 35 \\ x {}^{2} + 2x - 35 = 0 \\ \boxed{a = 1 \: , \: b = 2 \:, \: c = - 35} \\ x = \frac{ - b ± \sqrt{b {}^{2} - 4ac} }{2a} \\ x = \frac{ - 2 ± \sqrt{2 {}^{2} - 4 \: . \: 1 \: . \: ( - 35) } }{2 \: . \:1 } \\ x = \frac{ - 2 ± \sqrt{4 + 140} }{2} \\ x = \frac{ - 2 ± \sqrt{144} }{2} \\ x = \frac{ - 2 ± \sqrt{12} }{2} \\ x = \frac{ - 2 + 12}{2} = \frac{10}{2} = \boxed{\boxed{\boxed{5}}} \\ x = \frac{ - 2 - 12}{2} = \frac{ - 14}{2} = \boxed{\boxed{\boxed{ - 7}}}$

att. yrz