Solve x(x^2 7x-7)

Question

Simplify the expression

7 x^{4} - 7 x

Evaluate

x (x^{2} \times 7 x - 7)

Multiply

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Evaluate

x^{2} \times 7 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 7

Add the numbers

x^{3} \times 7

Use the commutative property to reorder the terms

7 x^{3}

x (7 x^{3} - 7)

Apply the distributive property

x \times 7 x^{3} - x \times 7

Multiply the terms

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Evaluate

x \times 7 x^{3}

Use the commutative property to reorder the terms

7 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}

7 x^{4}

7 x^{4} - x \times 7

Solution

7 x^{4} - 7 x

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Factor the expression

7 x (x - 1) (x^{2} + x + 1)

Evaluate

x (x^{2} \times 7 x - 7)

Multiply

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Evaluate

x^{2} \times 7 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 7

Add the numbers

x^{3} \times 7

Use the commutative property to reorder the terms

7 x^{3}

x (7 x^{3} - 7)

Factor the expression

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Evaluate

7 x^{3} - 7

Factor out 7 from the expression

7 (x^{3} - 1)

Factor the expression

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Evaluate

x^{3} - 1

Calculate

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

Rewrite the expression

x \times x^{2} + x \times x + x - x^{2} - x - 1

Factor out x from the expression

x (x^{2} + x + 1) - x^{2} - x - 1

Factor out - 1 from the expression

x (x^{2} + x + 1) - (x^{2} + x + 1)

Factor out x^{2} + x + 1 from the expression

(x - 1) (x^{2} + x + 1)

7 (x - 1) (x^{2} + x + 1)

x \times 7 (x - 1) (x^{2} + x + 1)

Solution

7 x (x - 1) (x^{2} + x + 1)

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Find the roots

x_{1} = 0, x_{2} = 1

Evaluate

x (x^{2} \times 7 x - 7)

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

x (x^{2} \times 7 x - 7) = 0

Multiply

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Multiply the terms

x^{2} \times 7 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 7

Add the numbers

x^{3} \times 7

Use the commutative property to reorder the terms

7 x^{3}

x (7 x^{3} - 7) = 0

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

7 x^{3} - 7 = 0

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

7 x^{3} = 0 + 7

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

7 x^{3} = 7

Divide both sides

\frac{7 x ^{3}}{7} = \frac{7}{7}

Divide the numbers

x^{3} = \frac{7}{7}

Divide the numbers

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Evaluate

\frac{7}{7}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{3} = 1

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

3 x^{3} = 31

Calculate

x = 31

Simplify the root

x = 1

x = 0 x = 1

Solution

x_{1} = 0, x_{2} = 1

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