What are the solutions to the equation x+6=x^3 ?

The solutions to the equation x+6=x^3 are x=2,x=-1+sqrt(2)i,x=-1-sqrt(2)i

Find the zeros of x+6=x^3

The zeros of x+6=x^3 are x=2,x=-1+sqrt(2)i,x=-1-sqrt(2)i

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x + 6 = x^{3}

x = 2, x = - 1 + 2 i, x = - 1 - 2 i

Solution steps

x + 6 = x^{3}

Switch sides

x^{3} = x + 6

Move

6

to the left side

x^{3} - 6 = x

Move

x

to the left side

x^{3} - 6 - x = 0

Write in the standard form

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

x^{3} - x - 6 = 0

Factor

x^{3} - x - 6 : (x - 2) (x^{2} + 2 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

x = 2, x = - 1 + 2 i, x = - 1 - 2 i

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

27 x^{4} + 60 x^{2} = 32

3 (x - 1) (x + 2) (x - 4) = 0

x^{4} - x^{3} + x = 1

- 2 x (x^{2} - 10) (x^{2} + 4) = 0

What are the solutions to the equation x+6=x^3 ?
The solutions to the equation x+6=x^3 are x=2,x=-1+sqrt(2)i,x=-1-sqrt(2)i
Find the zeros of x+6=x^3
The zeros of x+6=x^3 are x=2,x=-1+sqrt(2)i,x=-1-sqrt(2)i