What are the solutions to the equation 2x^4=2000x ?

The solutions to the equation 2x^4=2000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i

Find the zeros of 2x^4=2000x

The zeros of 2x^4=2000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i

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2 x^{4} = 2000 x

x = 0, x = 10, x = - 5 + 53 i, x = - 5 - 53 i

Solution steps

2 x^{4} = 2000 x

Move

2000 x

to the left side

2 x^{4} - 2000 x = 0

Factor

2 x^{4} - 2000 x : 2 x (x - 10) (x^{2} + 10 x + 100)

2 x (x - 10) (x^{2} + 10 x + 100) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 10 = 0 or x^{2} + 10 x + 100 = 0

Solve

x - 10 = 0 : x = 10

Solve

x^{2} + 10 x + 100 = 0 : x = - 5 + 53 i, x = - 5 - 53 i

The solutions are

x = 0, x = 10, x = - 5 + 53 i, x = - 5 - 53 i

x^{3} - 30 x^{2} + 297 x - 972 = 0

x^{2} (x + 2) = 0

x^{3} = 1 + 14 x

x^{4} + 9 x^{2} + 14 = 0

(x^{3} + 8) = 0

What are the solutions to the equation 2x^4=2000x ?
The solutions to the equation 2x^4=2000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i
Find the zeros of 2x^4=2000x
The zeros of 2x^4=2000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i