Solve (x 8)(x^27x-3)

Question

Simplify the expression

56 x^{4} - 24 x

Evaluate

(x \times 8) (x^{2} \times 7 x - 3)

Remove the parentheses

x \times 8 (x^{2} \times 7 x - 3)

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 \times 8 (7 x^{3} - 3)

Use the commutative property to reorder the terms

8 x (7 x^{3} - 3)

Apply the distributive property

8 x \times 7 x^{3} - 8 x \times 3

Multiply the terms

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Evaluate

8 x \times 7 x^{3}

Multiply the numbers

56 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}

56 x^{4}

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

Solution

56 x^{4} - 24 x

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 147}{7}

Alternative Form

x_{1} = 0, x_{2} \approx 0.753947

Evaluate

(x \times 8) (x^{2} \times 7 x - 3)

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

(x \times 8) (x^{2} \times 7 x - 3) = 0

Use the commutative property to reorder the terms

8 x (x^{2} \times 7 x - 3) = 0

Multiply

More Steps

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}

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

7 x^{3} - 3 = 0

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

7 x^{3} = 0 + 3

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

7 x^{3} = 3

Divide both sides

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

Divide the numbers

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

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

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

Calculate

x = 3 \frac{3}{7}

Simplify the root

More Steps

Evaluate

3 \frac{3}{7}

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

\frac{3 3}{3 7}

Multiply by the Conjugate

\frac{3 3 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 3 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

\frac{3 147}{3 7 \times 3 7 ^{2}}

Multiply the numbers

\frac{3 147}{7}

x = \frac{3 147}{7}

x = 0 x = \frac{3 147}{7}

Solution

x_{1} = 0, x_{2} = \frac{3 147}{7}

Alternative Form

x_{1} = 0, x_{2} \approx 0.753947

Show Solution