What are the solutions to the equation 8x^4=x ?

The solutions to the equation 8x^4=x are x=0,x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i

Find the zeros of 8x^4=x

The zeros of 8x^4=x are x=0,x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i

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8 x^{4} = x

x = 0, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Solution steps

8 x^{4} = x

Move

x

to the left side

8 x^{4} - x = 0

Factor

8 x^{4} - x : x (8 x^{3} - 1)

x (8 x^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

8 x^{3} - 1 = 0 : x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

The solutions are

x = 0, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

x^{5} + (2 - x)^{5} = 82

x^{3} - 5 x^{2} + 6 x = 0

(x^{2} + 1)^{3} = 0

2 x^{3} - 5 x^{2} + 1 = 0

(x + 2)^{4} + (x + 4)^{4} = 2

What are the solutions to the equation 8x^4=x ?
The solutions to the equation 8x^4=x are x=0,x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i
Find the zeros of 8x^4=x
The zeros of 8x^4=x are x=0,x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i