What are the solutions to the equation x^5=64x^2 ?

The solutions to the equation x^5=64x^2 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i

Find the zeros of x^5=64x^2

The zeros of x^5=64x^2 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i

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x^{5} = 64 x^{2}

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

Solution steps

x^{5} = 64 x^{2}

Move

64 x^{2}

to the left side

x^{5} - 64 x^{2} = 0

Factor

x^{5} - 64 x^{2} : x^{2} (x^{3} - 64)

x^{2} (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

- 16 x - 4 x^{3} = 164

20 x^{3} + 60 x^{2} = 0

x^{23} x + 2 = 0

2 x^{3} - 16 x^{2} - 40 x = 0

x^{3} = - 1000

What are the solutions to the equation x^5=64x^2 ?
The solutions to the equation x^5=64x^2 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i
Find the zeros of x^5=64x^2
The zeros of x^5=64x^2 are x=0,x=4,x=-2+2sqrt(3)i,x=-2-2sqrt(3)i