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

The solutions to the equation 3=x^3+2x are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2

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

The zeros of 3=x^3+2x are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2

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3 = x^{3} + 2 x

x = 1, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Solution steps

3 = x^{3} + 2 x

Switch sides

x^{3} + 2 x = 3

Move

3

to the left side

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

Factor

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

(x - 1) (x^{2} + x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + x + 3 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 3 = 0 : x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

2 x^{3} - x^{2} + 2 x - 1

6 x^{3} + 36 x - 12 = 0

x^{4} = x^{5}

(2 x + 1)^{3} = 900

11 x^{10} - 60 x^{9} = 0

What are the solutions to the equation 3=x^3+2x ?
The solutions to the equation 3=x^3+2x are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2
Find the zeros of 3=x^3+2x
The zeros of 3=x^3+2x are x=1,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2