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D( x )
x^2+8*x = 0
x^2+8*x = 0
x^2+8*x = 0
x^2+8*x = 0
DELTA = 8^2-(0*1*4)
DELTA = 64
DELTA > 0
x = (64^(1/2)-8)/(1*2) or x = (-64^(1/2)-8)/(1*2)
x = 0 or x = -8
x in (-oo:-8) U (-8:0) U (0:+oo)
x^2+8*x+7 = 144/(x^2+8*x) // - 144/(x^2+8*x)
x^2-(144/(x^2+8*x))+8*x+7 = 0
x^2-144*(x^2+8*x)^-1+8*x+7 = 0
x^2-144/(x^2+8*x)+8*x+7 = 0
x^2+8*x = 0
x^2+8*x = 0
x*(x+8) = 0
x+8 = 0 // - 8
x = -8
x*(x+8) = 0
x^2-144/(x*(x+8))+8*x+7 = 0
(x*x^2*(x+8))/(x*(x+8))-144/(x*(x+8))+(8*x*x*(x+8))/(x*(x+8))+(7*x*(x+8))/(x*(x+8)) = 0
x*x^2*(x+8)+8*x*x*(x+8)+7*x*(x+8)-144 = 0
x^4+8*x^3+8*x^3+64*x^2+7*x^2+56*x-144 = 0
x^4+16*x^3+64*x^2+7*x^2+56*x-144 = 0
x^4+16*x^3+71*x^2+56*x-144 = 0
x^4+16*x^3+71*x^2+56*x-144 = 0
x^4+16*x^3+71*x^2+56*x-144 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 16, -16, 18, -18, 24, -24, 36, -36, 48, -48, 72, -72, 144, -144 }
1
x = 1
x^4+16*x^3+71*x^2+56*x-144 = 0
1
x-1
x^3+17*x^2+88*x+144
x^4+16*x^3+71*x^2+56*x-144
x-1
x^3-x^4
17*x^3+71*x^2+56*x-144
17*x^2-17*x^3
88*x^2+56*x-144
88*x-88*x^2
144*x-144
144-144*x
0
x^3+17*x^2+88*x+144 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 16, -16, 18, -18, 24, -24, 36, -36, 48, -48, 72, -72, 144, -144 }
1
x = 1
x^3+17*x^2+88*x+144 = 250
1
-1
x = -1
x^3+17*x^2+88*x+144 = 72
-1
2
x = 2
x^3+17*x^2+88*x+144 = 396
2
-2
x = -2
x^3+17*x^2+88*x+144 = 28
-2
3
x = 3
x^3+17*x^2+88*x+144 = 588
3
-3
x = -3
x^3+17*x^2+88*x+144 = 6
-3
4
x = 4
x^3+17*x^2+88*x+144 = 832
4
-4
x = -4
x^3+17*x^2+88*x+144 = 0
-4
x+4
x^2+13*x+36
x^3+17*x^2+88*x+144
x+4
-x^3-4*x^2
13*x^2+88*x+144
-13*x^2-52*x
36*x+144
-36*x-144
0
x^2+13*x+36 = 0
DELTA = 13^2-(1*4*36)
DELTA = 25
DELTA > 0
x = (25^(1/2)-13)/(1*2) or x = (-25^(1/2)-13)/(1*2)
x = -4 or x = -9
x in { -9, -4, 1, -4}
(x+9)*(x+4)^2*(x-1) = 0
((x+9)*(x+4)^2*(x-1))/(x*(x+8)) = 0
((x+9)*(x+4)^2*(x-1))/(x*(x+8)) = 0 // * x*(x+8)
(x+9)*(x+4)^2*(x-1) = 0
( x+4 )
x+4 = 0 // - 4
x = -4
( x+9 )
x+9 = 0 // - 9
x = -9
( x-1 )
x-1 = 0 // + 1
x = 1
x in { -4, -4, -9, 1 }
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