What are the solutions to the equation x^3+2+x=0 ?

The solutions to the equation x^3+2+x=0 are x=-1,x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2

Find the zeros of x^3+2+x=0

The zeros of x^3+2+x=0 are x=-1,x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2

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x^{3} + 2 + x = 0

x = - 1, x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Solution steps

x^{3} + 2 + x = 0

Write in the standard form

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

x^{3} + x + 2 = 0

Factor

x^{3} + x + 2 : (x + 1) (x^{2} - x + 2)

(x + 1) (x^{2} - x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - x + 2 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} - x + 2 = 0 : x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

The solutions are

x = - 1, x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

\frac{2}{3} x^{3} - 18 = 0

x^{3} - 18 x - 8 = 0

e^{0.678} = x^{3}

384 = 3 (r^{8 - 1})

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

What are the solutions to the equation x^3+2+x=0 ?
The solutions to the equation x^3+2+x=0 are x=-1,x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2
Find the zeros of x^3+2+x=0
The zeros of x^3+2+x=0 are x=-1,x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2