What are the solutions to the equation x^3-x^2=18 ?

The solutions to the equation x^3-x^2=18 are x=3,x=-1+sqrt(5)i,x=-1-sqrt(5)i

Find the zeros of x^3-x^2=18

The zeros of x^3-x^2=18 are x=3,x=-1+sqrt(5)i,x=-1-sqrt(5)i

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x^{3} - x^{2} = 18

x = 3, x = - 1 + 5 i, x = - 1 - 5 i

Solution steps

x^{3} - x^{2} = 18

Move

18

to the left side

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

Factor

x^{3} - x^{2} - 18 : (x - 3) (x^{2} + 2 x + 6)

(x - 3) (x^{2} + 2 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 2 x + 6 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 2 x + 6 = 0 : x = - 1 + 5 i, x = - 1 - 5 i

The solutions are

x = 3, x = - 1 + 5 i, x = - 1 - 5 i

3 x^{3} = 7 x^{2} + 6 x

3 x^{4} - 24 x^{3} + 4 x^{2} - 29 x - 67 = 0

x^{3} + 2 x + 1

x^{3} + 2 x + 2

x^{6} - 3 x^{4} - x^{3} + 2 x^{2} - x - 1 = 0

What are the solutions to the equation x^3-x^2=18 ?
The solutions to the equation x^3-x^2=18 are x=3,x=-1+sqrt(5)i,x=-1-sqrt(5)i
Find the zeros of x^3-x^2=18
The zeros of x^3-x^2=18 are x=3,x=-1+sqrt(5)i,x=-1-sqrt(5)i