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D( x )
5*x+2 = 0
5*x+2 = 0
5*x+2 = 0
5*x+2 = 0 // - 2
5*x = -2 // : 5
x = -2/5
x in (-oo:-2/5) U (-2/5:+oo)
(20*x^3-(27*x^2)-(54*x)-16)/(5*x+2) = 0
(20*x^3-27*x^2-54*x-16)/(5*x+2) = 0
20*x^3-27*x^2-54*x-16 = 0
20*x^3-27*x^2-54*x-16 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }
1
x = 1
20*x^3-27*x^2-54*x-16 = -77
1
-1
x = -1
20*x^3-27*x^2-54*x-16 = -9
-1
2
x = 2
20*x^3-27*x^2-54*x-16 = -72
2
-2
x = -2
20*x^3-27*x^2-54*x-16 = -176
-2
4
x = 4
20*x^3-27*x^2-54*x-16 = 616
4
-4
x = -4
20*x^3-27*x^2-54*x-16 = -1512
-4
8
x = 8
20*x^3-27*x^2-54*x-16 = 8064
8
-8
x = -8
20*x^3-27*x^2-54*x-16 = -11552
-8
16
x = 16
20*x^3-27*x^2-54*x-16 = 74128
16
-16
x = -16
20*x^3-27*x^2-54*x-16 = -87984
-16
{ 1/2, -1/2, 1/4, -1/4, 1/5, -1/5, 1/10, -1/10, 1/20, -1/20, -1/2, 1/2, -1/4, 1/4, -1/5, 1/5, -1/10, 1/10, -1/20, 1/20, 2/2, -2/2, 2/4, -2/4, 2/5, -2/5, 2/10, -2/10, 2/20, -2/20, -2/2, 2/2, -2/4, 2/4, -2/5, 2/5, -2/10, 2/10, -2/20, 2/20, 4/2, -4/2, 4/4, -4/4, 4/5, -4/5, 4/10, -4/10, 4/20, -4/20, -4/2, 4/2, -4/4, 4/4, -4/5, 4/5, -4/10, 4/10, -4/20, 4/20, 8/2, -8/2, 8/4, -8/4, 8/5, -8/5, 8/10, -8/10, 8/20, -8/20, -8/2, 8/2, -8/4, 8/4, -8/5, 8/5, -8/10, 8/10, -8/20, 8/20, 16/2, -16/2, 16/4, -16/4, 16/5, -16/5, 16/10, -16/10, 16/20, -16/20, -16/2, 16/2, -16/4, 16/4, -16/5, 16/5, -16/10, 16/10, -16/20, 16/20 }
1/2
x
1/2
20*x^3-27*x^2-54*x-16 = -47.25
1/2
-1/2
x
-1/2
20*x^3-27*x^2-54*x-16 = 1.75
-1/2
1/4
x
1/4
20*x^3-27*x^2-54*x-16 = -30.875
1/4
-1/4
x
-1/4
20*x^3-27*x^2-54*x-16 = -4.5
-1/4
1/5
x
1/5
20*x^3-27*x^2-54*x-16 = -27.72
1/5
-1/5
x
-1/5
20*x^3-27*x^2-54*x-16 = -6.44
-1/5
1/10
x
1/10
20*x^3-27*x^2-54*x-16 = -21.65
1/10
-1/10
x
-1/10
20*x^3-27*x^2-54*x-16 = -10.89
-1/10
1/20
x
1/20
20*x^3-27*x^2-54*x-16 = -18.765
1/20
-1/20
x
-1/20
20*x^3-27*x^2-54*x-16 = -13.37
-1/20
-1/2
x
-1/2
20*x^3-27*x^2-54*x-16 = 1.75
-1/2
1/2
x
1/2
20*x^3-27*x^2-54*x-16 = -47.25
1/2
-1/4
x
-1/4
20*x^3-27*x^2-54*x-16 = -4.5
-1/4
1/4
x
1/4
20*x^3-27*x^2-54*x-16 = -30.875
1/4
-1/5
x
-1/5
20*x^3-27*x^2-54*x-16 = -6.44
-1/5
1/5
x
1/5
20*x^3-27*x^2-54*x-16 = -27.72
1/5
-1/10
x
-1/10
20*x^3-27*x^2-54*x-16 = -10.89
-1/10
1/10
x
1/10
20*x^3-27*x^2-54*x-16 = -21.65
1/10
-1/20
x
-1/20
20*x^3-27*x^2-54*x-16 = -13.37
-1/20
1/20
x
1/20
20*x^3-27*x^2-54*x-16 = -18.765
1/20
2/2
x
2/2
20*x^3-27*x^2-54*x-16 = -77
2/2
-2/2
x
-2/2
20*x^3-27*x^2-54*x-16 = -9
-2/2
2/4
x
2/4
20*x^3-27*x^2-54*x-16 = -47.25
2/4
-2/4
x
-2/4
20*x^3-27*x^2-54*x-16 = 1.75
-2/4
2/5
x
2/5
20*x^3-27*x^2-54*x-16 = -40.64
2/5
-2/5
x
-2/5
20*x^3-27*x^2-54*x-16 = 0
-2/5
x+2/5
20*x^2-35*x-40
20*x^3-27*x^2-54*x-16
x+2/5
-20*x^3-8*x^2
-35*x^2-54*x-16
35*x^2+14*x
-40*x-16
40*x+16
0
20*x^2-35*x-40 = 0
DELTA = (-35)^2-(-40*4*20)
DELTA = 4425
DELTA > 0
x = (4425^(1/2)+35)/(2*20) or x = (35-4425^(1/2))/(2*20)
x = (5*177^(1/2)+35)/40 or x = (35-5*177^(1/2))/40
x in { (35-5*177^(1/2))/40, (5*177^(1/2)+35)/40, -2/5}
(x-((35-5*177^(1/2))/40))*(x-((5*177^(1/2)+35)/40))*(x+2/5) = 0
((x-((35-5*177^(1/2))/40))*(x-((5*177^(1/2)+35)/40))*(x+2/5))/(5*x+2) = 0
( x+2/5 )
x+2/5 = 0 // - 2/5
x = -2/5
( x-((35-5*177^(1/2))/40) )
x-((35-5*177^(1/2))/40) = 0 // + (35-5*177^(1/2))/40
x = (35-5*177^(1/2))/40
( x-((5*177^(1/2)+35)/40) )
x-((5*177^(1/2)+35)/40) = 0 // + (5*177^(1/2)+35)/40
x = (5*177^(1/2)+35)/40
x in { -2/5}
x in { (35-5*177^(1/2))/40, (5*177^(1/2)+35)/40 }
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