What are the solutions to the equation x+x^3=2210 ?

The solutions to the equation x+x^3=2210 are x=13,x=-13/2+i(sqrt(511))/2 ,x=-13/2-i(sqrt(511))/2

Find the zeros of x+x^3=2210

The zeros of x+x^3=2210 are x=13,x=-13/2+i(sqrt(511))/2 ,x=-13/2-i(sqrt(511))/2

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x + x^{3} = 2210

x = 13, x = - \frac{13}{2} + i \frac{511}{2}, x = - \frac{13}{2} - i \frac{511}{2}

Solution steps

x + x^{3} = 2210

Move

2210

to the left side

x + x^{3} - 2210 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + x - 2210 = 0

Factor

x^{3} + x - 2210 : (x - 13) (x^{2} + 13 x + 170)

(x - 13) (x^{2} + 13 x + 170) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 13 = 0 or x^{2} + 13 x + 170 = 0

Solve

x - 13 = 0 : x = 13

Solve

x^{2} + 13 x + 170 = 0 : x = - \frac{13}{2} + i \frac{511}{2}, x = - \frac{13}{2} - i \frac{511}{2}

The solutions are

x = 13, x = - \frac{13}{2} + i \frac{511}{2}, x = - \frac{13}{2} - i \frac{511}{2}

t^{3} - 6 t^{2} = 2 t

63 x - 2 x^{2} - x^{3} = 0

x^{5} = 1024

4 x^{5} - x^{3} - 4 x^{2} + 1 = 0

x^{4} - 5 x^{2} - 44 = 0

What are the solutions to the equation x+x^3=2210 ?
The solutions to the equation x+x^3=2210 are x=13,x=-13/2+i(sqrt(511))/2 ,x=-13/2-i(sqrt(511))/2
Find the zeros of x+x^3=2210
The zeros of x+x^3=2210 are x=13,x=-13/2+i(sqrt(511))/2 ,x=-13/2-i(sqrt(511))/2