What are the solutions to the equation 6x^{32}=3x^{96} ?

The solutions to the equation 6x^{32}=3x^{96} are

Find the zeros of 6x^{32}=3x^{96}

The zeros of 6x^{32}=3x^{96} are

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6 x^{32} = 3 x^{96}

Solution steps

6 x^{32} = 3 x^{96}

Move

3 x^{96}

to the left side

6 x^{32} - 3 x^{96} = 0

Factor

6 x^{32} - 3 x^{96} : - 3 x^{32} (x + 642) (x - 642) (x^{2} + 322) (x^{2} + 2^{\frac{33}{64}} x + 322) (x^{2} - 2^{\frac{33}{64}} x + 322) (x^{16} + 2^{\frac{5}{8}} x^{8} + 42) (x^{16} - 2^{\frac{5}{8}} x^{8} + 42) (x^{8} + 2^{\frac{9}{16}} x^{4} + 82) (x^{8} - 2^{\frac{9}{16}} x^{4} + 82) (x^{4} + 2^{\frac{17}{32}} x^{2} + 162) (x^{4} - 2^{\frac{17}{32}} x^{2} + 162)

- 3 x^{32} (x + 642) (x - 642) (x^{2} + 322) (x^{2} + 2^{\frac{33}{64}} x + 322) (x^{2} - 2^{\frac{33}{64}} x + 322) (x^{16} + 2^{\frac{5}{8}} x^{8} + 42) (x^{16} - 2^{\frac{5}{8}} x^{8} + 42) (x^{8} + 2^{\frac{9}{16}} x^{4} + 82) (x^{8} - 2^{\frac{9}{16}} x^{4} + 82) (x^{4} + 2^{\frac{17}{32}} x^{2} + 162) (x^{4} - 2^{\frac{17}{32}} x^{2} + 162) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 642 = 0 or x - 642 = 0 or x^{2} + 322 = 0 or x^{2} + 2^{\frac{33}{64}} x + 322 = 0 or x^{2} - 2^{\frac{33}{64}} x + 322 = 0 or x^{16} + 2^{\frac{5}{8}} x^{8} + 42 = 0 or x^{16} - 2^{\frac{5}{8}} x^{8} + 42 = 0 or x^{8} + 2^{\frac{9}{16}} x^{4} + 82 = 0 or x^{8} - 2^{\frac{9}{16}} x^{4} + 82 = 0 or x^{4} + 2^{\frac{17}{32}} x^{2} + 162 = 0 or x^{4} - 2^{\frac{17}{32}} x^{2} + 162 = 0

Solve

x + 642 = 0 : x = - 642

Solve

x - 642 = 0 : x = 642

Solve

x^{2} + 322 = 0 : x = 322 i, x = - 322 i

Solve

x^{2} + 2^{\frac{33}{64}} x + 322 = 0 : x = - \frac{2 ^{\frac{33}{64}}}{2} + i \frac{2 ^{\frac{33}{64}}}{2}, x = - \frac{2 ^{\frac{33}{64}}}{2} - i \frac{2 ^{\frac{33}{64}}}{2}

Solve

x^{2} - 2^{\frac{33}{64}} x + 322 = 0 : x = \frac{2 ^{\frac{33}{64}}}{2} + i \frac{2 ^{\frac{33}{64}}}{2}, x = \frac{2 ^{\frac{33}{64}}}{2} - i \frac{2 ^{\frac{33}{64}}}{2}

Solve

x^{16} + 2^{\frac{5}{8}} x^{8} + 42 = 0 : x = 0.96736 \dots + \frac{1.04427 \dots - 0.84967 \dots}{2} i, x = - 0.96736 \dots - \frac{1.04427 \dots - 0.84967 \dots}{2} i, x = - 0.29344 \dots + \frac{0.84967 \dots + 1.04427 \dots}{2} i, x = 0.29344 \dots - \frac{0.84967 \dots + 1.04427 \dots}{2} i, x = 0.47652 \dots + \frac{0.56773 \dots + 1.04427 \dots}{2} i, x = - 0.47652 \dots - \frac{0.56773 \dots + 1.04427 \dots}{2} i, x = - 0.89152 \dots + \frac{1.04427 \dots - 0.56773 \dots}{2} i, x = 0.89152 \dots - \frac{1.04427 \dots - 0.56773 \dots}{2} i, x = 0.89152 \dots + \frac{1.04427 \dots - 0.56773 \dots}{2} i, x = - 0.89152 \dots - \frac{1.04427 \dots - 0.56773 \dots}{2} i, x = - 0.47652 \dots + \frac{0.56773 \dots + 1.04427 \dots}{2} i, x = 0.47652 \dots - \frac{0.56773 \dots + 1.04427 \dots}{2} i, x = 0.29344 \dots + \frac{0.84967 \dots + 1.04427 \dots}{2} i, x = - 0.29344 \dots - \frac{0.84967 \dots + 1.04427 \dots}{2} i, x = - 0.96736 \dots + \frac{1.04427 \dots - 0.84967 \dots}{2} i, x = 0.96736 \dots - \frac{1.04427 \dots - 0.84967 \dots}{2} i

Solve

x^{16} - 2^{\frac{5}{8}} x^{8} + 42 = 0 : x = 1.00602 \dots + \frac{1.04427 \dots - 1.00226 \dots}{2} i, x = - 1.00602 \dots - \frac{1.04427 \dots - 1.00226 \dots}{2} i, x = - 0.09908 \dots + \frac{1.00226 \dots + 1.04427 \dots}{2} i, x = 0.09908 \dots - \frac{1.00226 \dots + 1.04427 \dots}{2} i, x = 0.64130 \dots + \frac{0.19936 \dots + 1.04427 \dots}{2} i, x = - 0.64130 \dots - \frac{0.19936 \dots + 1.04427 \dots}{2} i, x = - 0.78142 \dots + \frac{1.04427 \dots - 0.19936 \dots}{2} i, x = 0.78142 \dots - \frac{1.04427 \dots - 0.19936 \dots}{2} i, x = 0.78142 \dots + \frac{1.04427 \dots - 0.19936 \dots}{2} i, x = - 0.78142 \dots - \frac{1.04427 \dots - 0.19936 \dots}{2} i, x = - 0.64130 \dots + \frac{0.19936 \dots + 1.04427 \dots}{2} i, x = 0.64130 \dots - \frac{0.19936 \dots + 1.04427 \dots}{2} i, x = 0.09908 \dots + \frac{1.00226 \dots + 1.04427 \dots}{2} i, x = - 0.09908 \dots - \frac{1.00226 \dots + 1.04427 \dots}{2} i, x = - 1.00602 \dots + \frac{1.04427 \dots - 1.00226 \dots}{2} i, x = 1.00602 \dots - \frac{1.04427 \dots - 1.00226 \dots}{2} i

Solve

x^{8} + 2^{\frac{9}{16}} x^{4} + 82 = 0 : x = 0.84052 \dots + \frac{1.04427 \dots - 0.39106 \dots}{2} i, x = - 0.84052 \dots - \frac{1.04427 \dots - 0.39106 \dots}{2} i, x = - 0.56161 \dots + \frac{0.39106 \dots + 1.04427 \dots}{2} i, x = 0.56161 \dots - \frac{0.39106 \dots + 1.04427 \dots}{2} i, x = 0.56161 \dots + \frac{0.39106 \dots + 1.04427 \dots}{2} i, x = - 0.56161 \dots - \frac{0.39106 \dots + 1.04427 \dots}{2} i, x = - 0.84052 \dots + \frac{1.04427 \dots - 0.39106 \dots}{2} i, x = 0.84052 \dots - \frac{1.04427 \dots - 0.39106 \dots}{2} i

Solve

x^{8} - 2^{\frac{9}{16}} x^{4} + 82 = 0 : x = 0.99146 \dots + \frac{1.04427 \dots - 0.94410 \dots}{2} i, x = - 0.99146 \dots - \frac{1.04427 \dots - 0.94410 \dots}{2} i, x = - 0.19721 \dots + \frac{0.94410 \dots + 1.04427 \dots}{2} i, x = 0.19721 \dots - \frac{0.94410 \dots + 1.04427 \dots}{2} i, x = 0.19721 \dots + \frac{0.94410 \dots + 1.04427 \dots}{2} i, x = - 0.19721 \dots - \frac{0.94410 \dots + 1.04427 \dots}{2} i, x = - 0.99146 \dots + \frac{1.04427 \dots - 0.94410 \dots}{2} i, x = 0.99146 \dots - \frac{1.04427 \dots - 0.94410 \dots}{2} i

Solve

x^{4} + 2^{\frac{17}{32}} x^{2} + 162 = 0 : x = \frac{1}{2 ^{\frac{15}{32}} \cdot 1.86787 \dots} + 0.93393 \dots i, x = - \frac{1}{2 ^{\frac{15}{32}} \cdot 1.86787 \dots} - 0.93393 \dots i, x = - \frac{1}{2 ^{\frac{15}{32}} \cdot 1.86787 \dots} + 0.93393 \dots i, x = \frac{1}{2 ^{\frac{15}{32}} \cdot 1.86787 \dots} - 0.93393 \dots i

Solve

x^{4} - 2^{\frac{17}{32}} x^{2} + 162 = 0 : x = \frac{1}{2 ^{\frac{15}{32}} \cdot 0.77370 \dots} + 0.38685 \dots i, x = - \frac{1}{2 ^{\frac{15}{32}} \cdot 0.77370 \dots} - 0.38685 \dots i, x = - \frac{1}{2 ^{\frac{15}{32}} \cdot 0.77370 \dots} + 0.38685 \dots i, x = \frac{1}{2 ^{\frac{15}{32}} \cdot 0.77370 \dots} - 0.38685 \dots i

The solutions are

2 x^{2} - 4 x^{5} = 0

6 x^{3} + 5 x^{2} - 4 x + 4 = 0

n^{3} - n = 5 n^{2} - 5

x^{3} - 8 = 0

x^{10000} = 12

What are the solutions to the equation 6x^{32}=3x^{96} ?
The solutions to the equation 6x^{32}=3x^{96} are
Find the zeros of 6x^{32}=3x^{96}
The zeros of 6x^{32}=3x^{96} are