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

The solutions to the equation x^3+3x^2=-x-3 are x=-3,x=i,x=-i

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

The zeros of x^3+3x^2=-x-3 are x=-3,x=i,x=-i

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

x = - 3, x = i, x = - i

Solution steps

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

Move

3

to the left side

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

Move

x

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 3 = 0 : x = - 3

Solve

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

The solutions are

x = - 3, x = i, x = - i

x^{3} - 8 x^{2} + 19 x - 12 = 0

x^{4} - 17 x + 16 = 0

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

8 x^{3} - 64 = 0

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

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