Solve 2x^34x^2 - x

Question

Simplify the expression

8 x^{5} - x

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

8 x^{3 + 2}

Add the numbers

8 x^{5}

8 x^{5} - x

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Factor the expression

x (8 x^{4} - 1)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

8 x^{3 + 2}

Add the numbers

8 x^{5}

8 x^{5} - x

Rewrite the expression

x \times 8 x^{4} - x

Solution

x (8 x^{4} - 1)

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Find the roots

x_{1} = - \frac{4 2}{2}, x_{2} = 0, x_{3} = \frac{4 2}{2}

Alternative Form

x_{1} \approx - 0.594604, x_{2} = 0, x_{3} \approx 0.594604

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

8 x^{3 + 2}

Add the numbers

8 x^{5}

8 x^{5} - x = 0

Factor the expression

x (8 x^{4} - 1) = 0

Separate the equation into 2 possible cases

x = 0 8 x^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

8 x^{4} - 1 = 0

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

8 x^{4} = 0 + 1

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

8 x^{4} = 1

Divide both sides

\frac{8 x ^{4}}{8} = \frac{1}{8}

Divide the numbers

x^{4} = \frac{1}{8}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{1}{8}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{8}

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

\frac{4 1}{4 8}

Simplify the radical expression

\frac{1}{4 8}

Multiply by the Conjugate

\frac{4 8 ^{3}}{4 8 \times 4 8 ^{3}}

Simplify

\frac{2 ^{2} 4 2}{4 8 \times 4 8 ^{3}}

Multiply the numbers

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

Reduce the fraction

\frac{4 2}{2}

x = \pm \frac{4 2}{2}

Separate the equation into 2 possible cases

x = \frac{4 2}{2} x = - \frac{4 2}{2}

x = 0 x = \frac{4 2}{2} x = - \frac{4 2}{2}

Solution

x_{1} = - \frac{4 2}{2}, x_{2} = 0, x_{3} = \frac{4 2}{2}

Alternative Form

x_{1} \approx - 0.594604, x_{2} = 0, x_{3} \approx 0.594604

Show Solution