What are the solutions to the equation x^3-3x^2=-2x+6 ?

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

Find the zeros of x^3-3x^2=-2x+6

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

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

x = 3, x = 2 i, x = - 2 i

Solution steps

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

Move

6

to the left side

x^{3} - 3 x^{2} - 6 = - 2 x

Move

2 x

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

x = 3, x = 2 i, x = - 2 i

z^{3} = 64

x^{3} + 7 x^{2} = 0

1000 = x (30 - 2 x) (20 - 2 x)

(x - 1)^{4} + 5 (x - 1)^{2} + 9 = 0

x, y^{2} = x^{3} + 7

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