Question

como se resolve essa equação de de 2 grau na forma geral ? x(x+23)+60=0

Answer 1

$x(x+23)+60=0\to \\\\ x^2+23x+60=0\\\\ x=1;\ b=23;\ c=60\\\\\\ \Delta=b^2-4ac\to \Delta=23^2-4.1.60\to \Delta=529-240\to \boxed{\Delta=289}\\\\ x' \neq x''\\\\\\ x= \dfrac{-b\pm \sqrt{\Delta} }{2a} \to ~~ x= \dfrac{-23\pm \sqrt{289} }{2.1} \to ~~ x= \dfrac{-23\pm 17 }{2} \to ~~\\\\\\ x'= \dfrac{-23+17 }{2} \to ~~x'= \dfrac{-6}{2} \to ~~\boxed{x'=-3}\\\\\\ x''= \dfrac{-23-17 }{2} \to ~~x''= \dfrac{-40 }{2} \to ~~\boxed{x''=-20}\\\\\\\\ \boxed{\boxed{S=\{-20~;~-3\}}}$

Answer 2

x .(x + 23) + 60 = 0

x² + 23x + 60 = 0

a=1 b=23 c=60

∆ = b² - 4 . a . c
∆ = 23² - 4 . 1 . 60
∆ = 529 - 240
∆ = 289


x = -b ± √∆
——————
2 . a

x = -23 ± √289
————————
2 . 1 x' = - 23 + 17 - 6
/ ————— = — =
x = -23 ± 17 / 2 2
——————
2 \ = - 3
\
x" = - 23 - 17
————— =
2

- 40
= ———— = - 20
2

S { -3 e -20}