Solve x^3 - 8x^24x^48

Question

Simplify the expression

x^{3} - 256 x^{6}

Evaluate

x^{3} - 8 x^{2} \times 4 x^{4} \times 8

Solution

More Steps

Evaluate

8 x^{2} \times 4 x^{4} \times 8

Multiply the terms

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Evaluate

8 \times 4 \times 8

Multiply the terms

32 \times 8

Multiply the numbers

256

256 x^{2} \times x^{4}

Multiply the terms with the same base by adding their exponents

256 x^{2 + 4}

Add the numbers

256 x^{6}

x^{3} - 256 x^{6}

Show Solution

Factor the expression

x^{3} (1 - 256 x^{3})

Evaluate

x^{3} - 8 x^{2} \times 4 x^{4} \times 8

Multiply

More Steps

Evaluate

8 x^{2} \times 4 x^{4} \times 8

Multiply the terms

More Steps

Evaluate

8 \times 4 \times 8

Multiply the terms

32 \times 8

Multiply the numbers

256

256 x^{2} \times x^{4}

Multiply the terms with the same base by adding their exponents

256 x^{2 + 4}

Add the numbers

256 x^{6}

x^{3} - 256 x^{6}

Rewrite the expression

x^{3} - x^{3} \times 256 x^{3}

Solution

x^{3} (1 - 256 x^{3})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 2}{8}

Alternative Form

x_{1} = 0, x_{2} \approx 0.15749

Evaluate

x^{3} - 8 x^{2} \times 4 x^{4} \times 8

To find the roots of the expression,set the expression equal to 0

x^{3} - 8 x^{2} \times 4 x^{4} \times 8 = 0

Multiply

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Multiply the terms

8 x^{2} \times 4 x^{4} \times 8

Multiply the terms

More Steps

Evaluate

8 \times 4 \times 8

Multiply the terms

32 \times 8

Multiply the numbers

256

256 x^{2} \times x^{4}

Multiply the terms with the same base by adding their exponents

256 x^{2 + 4}

Add the numbers

256 x^{6}

x^{3} - 256 x^{6} = 0

Factor the expression

x^{3} (1 - 256 x^{3}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 1 - 256 x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0 1 - 256 x^{3} = 0

Solve the equation

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Evaluate

1 - 256 x^{3} = 0

Move the constant to the right-hand side and change its sign

- 256 x^{3} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- 256 x^{3} = - 1

Change the signs on both sides of the equation

256 x^{3} = 1

Divide both sides

\frac{256 x ^{3}}{256} = \frac{1}{256}

Divide the numbers

x^{3} = \frac{1}{256}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{256}

Calculate

x = 3 \frac{1}{256}

Simplify the root

More Steps

Evaluate

3 \frac{1}{256}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 256}

Simplify the radical expression

\frac{1}{3 256}

Simplify the radical expression

\frac{1}{4 3 4}

Multiply by the Conjugate

\frac{3 4 ^{2}}{4 3 4 \times 3 4 ^{2}}

Simplify

\frac{2 3 2}{4 3 4 \times 3 4 ^{2}}

Multiply the numbers

\frac{2 3 2}{2 ^{4}}

Reduce the fraction

\frac{3 2}{2 ^{3}}

x = \frac{3 2}{2 ^{3}}

Simplify

x = \frac{3 2}{8}

x = 0 x = \frac{3 2}{8}

Solution

x_{1} = 0, x_{2} = \frac{3 2}{8}

Alternative Form

x_{1} = 0, x_{2} \approx 0.15749

Show Solution