What are the solutions to the equation x^4=512x ?

The solutions to the equation x^4=512x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i

Find the zeros of x^4=512x

The zeros of x^4=512x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i

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x^{4} = 512 x

x = 0, x = 8, x = - 4 + 43 i, x = - 4 - 43 i

Solution steps

x^{4} = 512 x

Move

512 x

to the left side

x^{4} - 512 x = 0

Factor

x^{4} - 512 x : x (x^{3} - 512)

x (x^{3} - 512) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 512 = 0

Solve

x^{3} - 512 = 0 : x = 8, x = - 4 + 43 i, x = - 4 - 43 i

The solutions are

x = 0, x = 8, x = - 4 + 43 i, x = - 4 - 43 i

(x - 2)^{3} - 9 = 18

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

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

10 + x + 2 x^{2} = x^{3}

2 = \frac{1}{4} r^{3}

What are the solutions to the equation x^4=512x ?
The solutions to the equation x^4=512x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i
Find the zeros of x^4=512x
The zeros of x^4=512x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i