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

The solutions to the equation 64x=x^4 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i

Find the zeros of 64x=x^4

The zeros of 64x=x^4 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i

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64 x = x^{4}

x = 0, x = 4, x = - 2 + 23 i, x = - 2 - 23 i

Solution steps

64 x = x^{4}

Switch sides

x^{4} = 64 x

Move

64 x

to the left side

x^{4} - 64 x = 0

Factor

x^{4} - 64 x : x (x^{3} - 64)

x (x^{3} - 64) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 64 = 0

Solve

x^{3} - 64 = 0 : x = 4, x = - 2 + 23 i, x = - 2 - 23 i

The solutions are

x = 0, x = 4, x = - 2 + 23 i, x = - 2 - 23 i

6 x^{3} - 11 x^{2} - 9 x - 1 = 0

30 x^{4} - 120 x^{3} = 0

4 x^{3} - 12 x^{2} - 9 x - 1 = 0

2 x^{3} + 3 x^{2} - 12 x + 1 = 0

x^{3} - 2 x^{2} - 25 x + 50 = 0

What are the solutions to the equation 64x=x^4 ?
The solutions to the equation 64x=x^4 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i
Find the zeros of 64x=x^4
The zeros of 64x=x^4 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i