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

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Numerical solution:

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The solution

You have entered [src]
 5              
x  + 2*x + 4 = 0
$$\left(x^{5} + 2 x\right) + 4 = 0$$
The graph
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
$$\left(\left(1.12609445146789 - 0.921163549101315 i\right) + \left(\left(-1.11976260939548 + \left(-0.566213146770154 - 1.16922106879293 i\right)\right) + \left(-0.566213146770154 + 1.16922106879293 i\right)\right)\right) + \left(1.12609445146789 + 0.921163549101315 i\right)$$
=
0
$$0$$
product
-1.11976260939548*(-0.566213146770154 - 1.16922106879293*I)*(-0.566213146770154 + 1.16922106879293*I)*(1.12609445146789 - 0.921163549101315*I)*(1.12609445146789 + 0.921163549101315*I)
$$- 1.11976260939548 \left(-0.566213146770154 - 1.16922106879293 i\right) \left(-0.566213146770154 + 1.16922106879293 i\right) \left(1.12609445146789 - 0.921163549101315 i\right) \left(1.12609445146789 + 0.921163549101315 i\right)$$
=
-4.00000000000000
$$-4.0$$
-4.00000000000000
Rapid solution [src]
x1 = -1.11976260939548
$$x_{1} = -1.11976260939548$$
x2 = -0.566213146770154 - 1.16922106879293*I
$$x_{2} = -0.566213146770154 - 1.16922106879293 i$$
x3 = -0.566213146770154 + 1.16922106879293*I
$$x_{3} = -0.566213146770154 + 1.16922106879293 i$$
x4 = 1.12609445146789 - 0.921163549101315*I
$$x_{4} = 1.12609445146789 - 0.921163549101315 i$$
x5 = 1.12609445146789 + 0.921163549101315*I
$$x_{5} = 1.12609445146789 + 0.921163549101315 i$$
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