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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
x^2+x-(30/x)-5 = 11 // - 11
x^2+x-(30/x)-11-5 = 0
x^2+x-30*x^-1-11-5 = 0
1*x^2+1*x^1-30*x^-1-16*x^0 = 0
(1*x^3+1*x^2-16*x^1-30*x^0)/(x^1) = 0 // * x^2
x^1*(1*x^3+1*x^2-16*x^1-30*x^0) = 0
x^1
x^3+x^2-16*x-30 = 0
{ 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 30, -30 }
1
x = 1
x^3+x^2-16*x-30 = -44
1
-1
x = -1
x^3+x^2-16*x-30 = -14
-1
2
x = 2
x^3+x^2-16*x-30 = -50
2
-2
x = -2
x^3+x^2-16*x-30 = -2
-2
3
x = 3
x^3+x^2-16*x-30 = -42
3
-3
x = -3
x^3+x^2-16*x-30 = 0
-3
x+3
x^2-2*x-10
x^3+x^2-16*x-30
x+3
-x^3-3*x^2
-2*x^2-16*x-30
2*x^2+6*x
-10*x-30
10*x+30
0
x^2-2*x-10 = 0
DELTA = (-2)^2-(-10*1*4)
DELTA = 44
DELTA > 0
x = (44^(1/2)+2)/(1*2) or x = (2-44^(1/2))/(1*2)
x = (2*11^(1/2)+2)/2 or x = (2-2*11^(1/2))/2
x in { (2-2*11^(1/2))/2, (2*11^(1/2)+2)/2, -3}
x in { (2-2*11^(1/2))/2, (2*11^(1/2)+2)/2, -3 }
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