Question

Resolva as seguintes equações do 2 grau ?

A) ( x+5).(x-10)=0 B) (2x+1).(3x-27)=0

Answer 1

A)
$( x+5)(x-10)=0\\x^2-10x+5x-50=0\\x^2-5x^2-50=0$

$x= \frac{-(-5)\pm \sqrt{(-5)^2-4(-50)} }{2}= \frac{5\pm15}{2}$

$x_{1}=\frac{5-15}{2}=- \frac{10}{2}=-5$

$x_{2}= \frac{5+15}{2} = \frac{20}{2}=10$

$S=\{-5,10\}$


B)
$(2x+1)(3x-27)=0\\6x^2-54x+3x-27=0\\6x^2-51x-27=0$

$x= \frac{-(-51)\pm \sqrt{(-51)^2-4\cdot6(-27)} }{2\cdot6}= \frac{51\pm57}{12}$

$x_{1}=\frac{51-57}{12}=- \frac{6}{12}=- \frac{1}{2}$

$\frac{51+57}{12}= \frac{108}{12}=9$

$S=\{- \frac{1}{2},9\}$