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(x^5)+2x+4=0 equation

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Numerical solution:

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The solution

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 5              
x  + 2*x + 4 = 0
(x5+2x)+4=0\left(x^{5} + 2 x\right) + 4 = 0
Simplify
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.5-200000200000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1.11976260939548 + -0.566213146770154 - 1.16922106879293*I + -0.566213146770154 + 1.16922106879293*I + 1.12609445146789 - 0.921163549101315*I + 1.12609445146789 + 0.921163549101315*I
((1.12609445146789−0.921163549101315i)+((−1.11976260939548+(−0.566213146770154−1.16922106879293i))+(−0.566213146770154+1.16922106879293i)))+(1.12609445146789+0.921163549101315i)\left(\left(1.12609445146789 - 0.921163549101315 i\right) + \left(\left(-1.11976260939548 + \left(-0.566213146770154 - 1.16922106879293 i\right)\right) + \left(-0.566213146770154 + 1.16922106879293 i\right)\right)\right) + \left(1.12609445146789 + 0.921163549101315 i\right) 
=
0
00 
product
-1.11976260939548*(-0.566213146770154 - 1.16922106879293*I)*(-0.566213146770154 + 1.16922106879293*I)*(1.12609445146789 - 0.921163549101315*I)*(1.12609445146789 + 0.921163549101315*I)
−1.11976260939548(−0.566213146770154−1.16922106879293i)(−0.566213146770154+1.16922106879293i)(1.12609445146789−0.921163549101315i)(1.12609445146789+0.921163549101315i)- 1.11976260939548 \left(-0.566213146770154 - 1.16922106879293 i\right) \left(-0.566213146770154 + 1.16922106879293 i\right) \left(1.12609445146789 - 0.921163549101315 i\right) \left(1.12609445146789 + 0.921163549101315 i\right) 
=
-4.00000000000000
−4.0-4.0 
-4.00000000000000
Rapid solution [src] 
x1 = -1.11976260939548
x1=−1.11976260939548x_{1} = -1.11976260939548 
x2 = -0.566213146770154 - 1.16922106879293*I
x2=−0.566213146770154−1.16922106879293ix_{2} = -0.566213146770154 - 1.16922106879293 i 
x3 = -0.566213146770154 + 1.16922106879293*I
x3=−0.566213146770154+1.16922106879293ix_{3} = -0.566213146770154 + 1.16922106879293 i 
x4 = 1.12609445146789 - 0.921163549101315*I
x4=1.12609445146789−0.921163549101315ix_{4} = 1.12609445146789 - 0.921163549101315 i 
x5 = 1.12609445146789 + 0.921163549101315*I
x5=1.12609445146789+0.921163549101315ix_{5} = 1.12609445146789 + 0.921163549101315 i 
x5 = 1.12609445146789 + 0.921163549101315*i
Numerical answer [src] 
x1 = -1.11976260939548
x2 = 1.12609445146789 + 0.921163549101315*i
x3 = -0.566213146770154 - 1.16922106879293*i
x4 = -0.566213146770154 + 1.16922106879293*i
x5 = 1.12609445146789 - 0.921163549101315*i
x5 = 1.12609445146789 - 0.921163549101315*i
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