Question

Determine o conjunto solução das equaçoes do 2 grau :

a) 10$x^{2}$+25x=0

b)5x(x+3)+(x-3)²=9

c)$x^{2}$+6x(x-1)=0

Answer 1

a)
10x² + 25x = 0
x.(10x + 25) = 0
x = 0

10x + 25 = 0
10x = - 25
x = - 25  (:5)       - 5
     --------       =  ------
       10   (:5)         2

R.: x = 0 e x = - 5/2

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
5x.(x + 3) + (x - 3)² = 9
5x² + 15x + x² - 2.3x + 9 = 9
5x² + 15x + x² - 6x = 9 - 9
5x² + x² + 15x - 6x = 0
6x² + 9x = 0
x.(6x + 9) = 0
x = 0

6x + 9 = 0
6x = - 9
x = - 9   (:3)       - 3
     ------         =  ------
         6  (:3)          2

R.: x = 0 e x = - 3/2

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)

x² + 6x.(x - 1) = 0
x² + 6x² - 6 = 0
7x² = 6
x² = 6
      -----
       7

x = +/- √6/7
        ___             ____
x = √6/7 e x = - √6/7