What are the solutions to the equation 2x=16x^4 ?

The solutions to the equation 2x=16x^4 are x=0,x= 1/2 ,x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4

Find the zeros of 2x=16x^4

The zeros of 2x=16x^4 are x=0,x= 1/2 ,x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4

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2 x = 16 x^{4}

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

Solution steps

2 x = 16 x^{4}

Move

16 x^{4}

to the left side

2 x - 16 x^{4} = 0

Factor

2 x - 16 x^{4} : - 2 x (2 x - 1) (4 x^{2} + 2 x + 1)

- 2 x (2 x - 1) (4 x^{2} + 2 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 x - 1 = 0 or 4 x^{2} + 2 x + 1 = 0

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

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

The solutions are

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

2 x^{3} + 1 = x^{2} + 2

x^{3} - 7 x^{2} + x - 7 = 0

x^{3} = \frac{1}{8}

x^{3} - 6 x^{2} - 16 x + 96 = 0

(q) = q^{3} - 30 q^{2} + 500 q - 200

What are the solutions to the equation 2x=16x^4 ?
The solutions to the equation 2x=16x^4 are x=0,x= 1/2 ,x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4
Find the zeros of 2x=16x^4
The zeros of 2x=16x^4 are x=0,x= 1/2 ,x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4