What are the solutions to the equation x^3-27=x-3 ?

The solutions to the equation x^3-27=x-3 are x=3,x=-3/2+i(sqrt(23))/2 ,x=-3/2-i(sqrt(23))/2

Find the zeros of x^3-27=x-3

The zeros of x^3-27=x-3 are x=3,x=-3/2+i(sqrt(23))/2 ,x=-3/2-i(sqrt(23))/2

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x^{3} - 27 = x - 3

x = 3, x = - \frac{3}{2} + i \frac{23}{2}, x = - \frac{3}{2} - i \frac{23}{2}

Solution steps

x^{3} - 27 = x - 3

Move

3

to the left side

x^{3} - 24 = x

Move

x

to the left side

x^{3} - 24 - x = 0

Write in the standard form

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

x^{3} - x - 24 = 0

Factor

x^{3} - x - 24 : (x - 3) (x^{2} + 3 x + 8)

(x - 3) (x^{2} + 3 x + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 3 x + 8 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 3 x + 8 = 0 : x = - \frac{3}{2} + i \frac{23}{2}, x = - \frac{3}{2} - i \frac{23}{2}

The solutions are

x = 3, x = - \frac{3}{2} + i \frac{23}{2}, x = - \frac{3}{2} - i \frac{23}{2}

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

s \cdot (s + 2) \cdot (s + 4) - 6 = 0

(x - 5)^{3} - x + 5 = 0

(x^{3} + 1)^{3} = 8 (2 x - 1)

2 x^{3} + 5 x^{2} - 25 x = 0

What are the solutions to the equation x^3-27=x-3 ?
The solutions to the equation x^3-27=x-3 are x=3,x=-3/2+i(sqrt(23))/2 ,x=-3/2-i(sqrt(23))/2
Find the zeros of x^3-27=x-3
The zeros of x^3-27=x-3 are x=3,x=-3/2+i(sqrt(23))/2 ,x=-3/2-i(sqrt(23))/2