What are the solutions to the equation x^3-64=x-4 ?

The solutions to the equation x^3-64=x-4 are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i

Find the zeros of x^3-64=x-4

The zeros of x^3-64=x-4 are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i

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x^{3} - 64 = x - 4

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

Solution steps

x^{3} - 64 = x - 4

Move

4

to the left side

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

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

3 x^{3} + 4 = x^{2} + 12 x

8 x^{3} - 6 x - 1 = 0

x^{4} = 64

3 a^{5} - a^{2} = 120

What are the solutions to the equation x^3-64=x-4 ?
The solutions to the equation x^3-64=x-4 are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i
Find the zeros of x^3-64=x-4
The zeros of x^3-64=x-4 are x=4,x=-2+sqrt(11)i,x=-2-sqrt(11)i