What are the solutions to the equation x^3-60=x ?

The solutions to the equation x^3-60=x are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i

Find the zeros of x^3-60=x

The zeros of x^3-60=x are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i

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x^{3} - 60 = x

x = 4, x = - 2 + 11 i, x = - 2 - 11 i

Solution steps

x^{3} - 60 = x

Move

x

to the left side

x^{3} - 60 - x = 0

Write in the standard form

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

x^{3} - x - 60 = 0

Factor

x^{3} - x - 60 : (x - 4) (x^{2} + 4 x + 15)

(x - 4) (x^{2} + 4 x + 15) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} + 4 x + 15 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} + 4 x + 15 = 0 : x = - 2 + 11 i, x = - 2 - 11 i

The solutions are

x = 4, x = - 2 + 11 i, x = - 2 - 11 i

4 x^{3} - 10 x = 0

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

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

x^{11} = 2

λ^{3} - 6 λ^{2} + 11 λ - 6 = 0

What are the solutions to the equation x^3-60=x ?
The solutions to the equation x^3-60=x are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i
Find the zeros of x^3-60=x
The zeros of x^3-60=x are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i