Question

( URGENTE ) 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)
10 x^{2} +25x=0
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
x = - 9  (:3)        - 3
      -----        =  ------- 
         6  (:3)          2

R.: x = 0 e x = - 3/2

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c)
x^{2} +6x(x - 1) = 0

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

7x - 6 = 0
7x = 6
x = 6/7

R.: x = 0 e x = 6/7