What are the solutions to the equation solvefor x,x^3-7x^2=7-x ?

The solutions to the equation solvefor x,x^3-7x^2=7-x are x=7,x=i,x=-i

Find the zeros of solvefor x,x^3-7x^2=7-x

The zeros of solvefor x,x^3-7x^2=7-x are x=7,x=i,x=-i

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solve for

x, x^{3} - 7 x^{2} = 7 - x

x = 7, x = i, x = - i

Solution steps

x^{3} - 7 x^{2} = 7 - x

Move

x

to the left side

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

Move

7

to the left side

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

Factor

x^{3} - 7 x^{2} + x - 7 : (x - 7) (x^{2} + 1)

(x - 7) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 7 = 0 or x^{2} + 1 = 0

Solve

x - 7 = 0 : x = 7

Solve

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

The solutions are

x = 7, x = i, x = - i

x^{4} - 4 x^{3} + 4 x^{2} - 36 x - 45 = 0

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

x^{3} - 9 x^{2} + 31 x - 39

4 x^{3} - 18 x^{2} + 24 x = 0

x^{3} - 2 - 2 \times i = 0

What are the solutions to the equation solvefor x,x^3-7x^2=7-x ?
The solutions to the equation solvefor x,x^3-7x^2=7-x are x=7,x=i,x=-i
Find the zeros of solvefor x,x^3-7x^2=7-x
The zeros of solvefor x,x^3-7x^2=7-x are x=7,x=i,x=-i