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D( x )
4*x+2 = 0
4*x+2 = 0
4*x+2 = 0
4*x+2 = 0 // - 2
4*x = -2 // : 4
x = -2/4
x = -1/2
x in (-oo:-1/2) U (-1/2:+oo)
(8*x^3-(28*x^2)-(20*x)-2)/(4*x+2) = 0
(8*x^3-28*x^2-20*x-2)/(4*x+2) = 0
8*x^3-28*x^2-20*x-2 = 0
2*(4*x^3-14*x^2-10*x-1) = 0
4*x^3-14*x^2-10*x-1 = 0
{ 1, -1 }
1
x = 1
4*x^3-14*x^2-10*x-1 = -21
1
-1
x = -1
4*x^3-14*x^2-10*x-1 = -9
-1
{ 1/2, -1/2, 1/4, -1/4, -1/2, 1/2, -1/4, 1/4 }
1/2
x
1/2
4*x^3-14*x^2-10*x-1 = -9
1/2
-1/2
x
-1/2
4*x^3-14*x^2-10*x-1 = 0
-1/2
x+1/2
4*x^2-16*x-2
4*x^3-14*x^2-10*x-1
x+1/2
-4*x^3-2*x^2
-16*x^2-10*x-1
16*x^2+8*x
-2*x-1
2*x+1
0
4*x^2-16*x-2 = 0
DELTA = (-16)^2-(-2*4*4)
DELTA = 288
DELTA > 0
x = (288^(1/2)+16)/(2*4) or x = (16-288^(1/2))/(2*4)
x = (12*2^(1/2)+16)/8 or x = (16-12*2^(1/2))/8
x in { (16-12*2^(1/2))/8, (12*2^(1/2)+16)/8, -1/2}
2*(x-((16-12*2^(1/2))/8))*(x-((12*2^(1/2)+16)/8))*(x+1/2) = 0
(2*(x-((16-12*2^(1/2))/8))*(x-((12*2^(1/2)+16)/8))*(x+1/2))/(4*x+2) = 0
( x+1/2 )
x+1/2 = 0 // - 1/2
x = -1/2
( x-((12*2^(1/2)+16)/8) )
x-((12*2^(1/2)+16)/8) = 0 // + (12*2^(1/2)+16)/8
x = (12*2^(1/2)+16)/8
( x-((16-12*2^(1/2))/8) )
x-((16-12*2^(1/2))/8) = 0 // + (16-12*2^(1/2))/8
x = (16-12*2^(1/2))/8
x in { -1/2}
x in { (12*2^(1/2)+16)/8, (16-12*2^(1/2))/8 }
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