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D( x )
(4*x+5)^3 = 0
(4*x+5)^3 = 0
(4*x+5)^3 = 0
4*x+5 = 0 // - 5
4*x = -5 // : 4
x = -5/4
x in (-oo:-5/4) U (-5/4:+oo)
(6*(4*x+5)*(2*x+5)^2-8*(2*x+5)^3)/((4*x+5)^3) = 0
6*(4*x+5)*(2*x+5)^2-8*(2*x+5)^3 = 0
6*(4*x+5)*(2*x+5)^2-8*(2*x+5)^3 = 0
32*x^3+120*x^2-250 = 0
32*x^3+120*x^2-250 = 0
2*(16*x^3+60*x^2-125) = 0
16*x^3+60*x^2-125 = 0
{ 1, -1, 5, -5, 25, -25, 125, -125 }
1
x = 1
16*x^3+60*x^2-125 = -49
1
-1
x = -1
16*x^3+60*x^2-125 = -81
-1
5
x = 5
16*x^3+60*x^2-125 = 3375
5
-5
x = -5
16*x^3+60*x^2-125 = -625
-5
25
x = 25
16*x^3+60*x^2-125 = 287375
25
-25
x = -25
16*x^3+60*x^2-125 = -212625
-25
125
x = 125
16*x^3+60*x^2-125 = 32187375
125
-125
x = -125
16*x^3+60*x^2-125 = -30312625
-125
{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, 1/16, -1/16, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8, -1/16, 1/16, 5/2, -5/2, 5/4, -5/4, 5/8, -5/8, 5/16, -5/16, -5/2, 5/2, -5/4, 5/4, -5/8, 5/8, -5/16, 5/16, 25/2, -25/2, 25/4, -25/4, 25/8, -25/8, 25/16, -25/16, -25/2, 25/2, -25/4, 25/4, -25/8, 25/8, -25/16, 25/16, 125/2, -125/2, 125/4, -125/4, 125/8, -125/8, 125/16, -125/16, -125/2, 125/2, -125/4, 125/4, -125/8, 125/8, -125/16, 125/16 }
1/2
x
1/2
16*x^3+60*x^2-125 = -108
1/2
-1/2
x
-1/2
16*x^3+60*x^2-125 = -112
-1/2
1/4
x
1/4
16*x^3+60*x^2-125 = -121
1/4
-1/4
x
-1/4
16*x^3+60*x^2-125 = -121.5
-1/4
1/8
x
1/8
16*x^3+60*x^2-125 = -124.03125
1/8
-1/8
x
-1/8
16*x^3+60*x^2-125 = -124.09375
-1/8
1/16
x
1/16
16*x^3+60*x^2-125 = -124.76171875
1/16
-1/16
x
-1/16
16*x^3+60*x^2-125 = -124.76953125
-1/16
-1/2
x
-1/2
16*x^3+60*x^2-125 = -112
-1/2
1/2
x
1/2
16*x^3+60*x^2-125 = -108
1/2
-1/4
x
-1/4
16*x^3+60*x^2-125 = -121.5
-1/4
1/4
x
1/4
16*x^3+60*x^2-125 = -121
1/4
-1/8
x
-1/8
16*x^3+60*x^2-125 = -124.09375
-1/8
1/8
x
1/8
16*x^3+60*x^2-125 = -124.03125
1/8
-1/16
x
-1/16
16*x^3+60*x^2-125 = -124.76953125
-1/16
1/16
x
1/16
16*x^3+60*x^2-125 = -124.76171875
1/16
5/2
x
5/2
16*x^3+60*x^2-125 = 500
5/2
-5/2
x
-5/2
16*x^3+60*x^2-125 = 0
-5/2
x+5/2
16*x^2+20*x-50
16*x^3+60*x^2-125
x+5/2
-16*x^3-40*x^2
20*x^2-125
-20*x^2-50*x
-50*x-125
50*x+125
0
16*x^2+20*x-50 = 0
DELTA = 20^2-(-50*4*16)
DELTA = 3600
DELTA > 0
x = (3600^(1/2)-20)/(2*16) or x = (-3600^(1/2)-20)/(2*16)
x = 5/4 or x = -5/2
x in { -5/2, 5/4, -5/2}
2*(x+5/2)^2*(x-5/4) = 0
2*(x+5/2)^2*(x-5/4) = 0
(2*(x+5/2)^2*(x-5/4))/((4*x+5)^3) = 0
( x+5/2 )
x+5/2 = 0 // - 5/2
x = -5/2
( x-5/4 )
x-5/4 = 0 // + 5/4
x = 5/4
x in { -5/2, -5/2, 5/4 }
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