Question

Equações

A) 2x.(2x-4) = 4.(2x+12)

B) 3x ao quadrado-2x-4 = 2x.(x+6)-4

C)x ao quadrado- ½x = 0

Answer 1

A)
2x.(2x - 4) = 4.(2x + 12)
x.(2x - 4) = 4.(2x + 12)/2
2x^2 - 4x = 2.(2x + 12)
2(x^2 - 2x) = 2.(2x + 12)
x^2 - 2x = 2x + 12
x^2 - 2x - 2x - 12 = 0
x^2 - 4x - 12 = 0
a = 1; b = - 4; c = - 12
∆ = b^2-4ac
∆ = (-4)^2 - 4.1.(-12)
∆ = 16 + 48
∆ = 64

x = [ - b +/- √∆[/2a
x = [ -(-4) +/- √64]/2.1
x = [ 4 +/- 8]/2
x' = [4 + 8]/2 = 12/2 = 6
x" = [4 - 8]/2 = - 4/2 = - 2

R.: x = 6; x = - 2

B)
3x^2 - 2x - 4 = 2x.(x + 6) - 4
3x^2 - 2x - 4 = 2x^2 + 12x - 4
3x^2 - 2x - 2x^2 - 12x = - 4 + 4
x^2 - 14x = 0
x.(x - 14) = 0
x = 0
x - 14 = 0
x = 14

R.: x = 0; x = 14

C)
x^2 - ½x = 0
(2x^2 - 1x)/2 = 0/2
2x^2 - x = 0
x.(2x - 1) = 0
x = 0
2x - 1 = 0
2x = 1
x = 1/2

R.: x = 0; x = 1/2