Solve (2x-1)(x^25x-1)

Question

Simplify the expression

10 x^{4} - 2 x - 5 x^{3} + 1

Evaluate

(2 x - 1) (x^{2} \times 5 x - 1)

Multiply

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Evaluate

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

(2 x - 1) (5 x^{3} - 1)

Apply the distributive property

2 x \times 5 x^{3} - 2 x \times 1 - 5 x^{3} - (- 1)

Multiply the terms

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Evaluate

2 x \times 5 x^{3}

Multiply the numbers

10 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 3}

Add the numbers

x^{4}

10 x^{4}

10 x^{4} - 2 x \times 1 - 5 x^{3} - (- 1)

Any expression multiplied by 1 remains the same

10 x^{4} - 2 x - 5 x^{3} - (- 1)

Solution

10 x^{4} - 2 x - 5 x^{3} + 1

Show Solution

Find the roots

x_{1} = \frac{1}{2}, x_{2} = \frac{3 25}{5}

Alternative Form

x_{1} = 0.5, x_{2} \approx 0.584804

Evaluate

(2 x - 1) (x^{2} \times 5 x - 1)

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

(2 x - 1) (x^{2} \times 5 x - 1) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

(2 x - 1) (5 x^{3} - 1) = 0

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = \frac{1}{2} 5 x^{3} - 1 = 0

Solve the equation

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Evaluate

5 x^{3} - 1 = 0

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

5 x^{3} = 0 + 1

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

5 x^{3} = 1

Divide both sides

\frac{5 x ^{3}}{5} = \frac{1}{5}

Divide the numbers

x^{3} = \frac{1}{5}

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

3 x^{3} = 3 \frac{1}{5}

Calculate

x = 3 \frac{1}{5}

Simplify the root

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Evaluate

3 \frac{1}{5}

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

\frac{3 1}{3 5}

Simplify the radical expression

\frac{1}{3 5}

Multiply by the Conjugate

\frac{3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 25}{5}

x = \frac{3 25}{5}

x = \frac{1}{2} x = \frac{3 25}{5}

Solution

x_{1} = \frac{1}{2}, x_{2} = \frac{3 25}{5}

Alternative Form

x_{1} = 0.5, x_{2} \approx 0.584804

Show Solution