Solve (x^3)(3x^(2) 7x-5)

Question

Simplify the expression

21 x^{6} - 5 x^{3}

Evaluate

x^{3} (3 x^{2} \times 7 x - 5)

Multiply

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Evaluate

3 x^{2} \times 7 x

Multiply the terms

21 x^{2} \times x

Multiply the terms with the same base by adding their exponents

21 x^{2 + 1}

Add the numbers

21 x^{3}

x^{3} (21 x^{3} - 5)

Apply the distributive property

x^{3} \times 21 x^{3} - x^{3} \times 5

Multiply the terms

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Evaluate

x^{3} \times 21 x^{3}

Use the commutative property to reorder the terms

21 x^{3} \times x^{3}

Multiply the terms

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Evaluate

x^{3} \times x^{3}

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

x^{3 + 3}

Add the numbers

x^{6}

21 x^{6}

21 x^{6} - x^{3} \times 5

Solution

21 x^{6} - 5 x^{3}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 2205}{21}

Alternative Form

x_{1} = 0, x_{2} \approx 0.619798

Evaluate

(x^{3}) (3 x^{2} \times 7 x - 5)

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

(x^{3}) (3 x^{2} \times 7 x - 5) = 0

Calculate

x^{3} (3 x^{2} \times 7 x - 5) = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 7 x

Multiply the terms

21 x^{2} \times x

Multiply the terms with the same base by adding their exponents

21 x^{2 + 1}

Add the numbers

21 x^{3}

x^{3} (21 x^{3} - 5) = 0

Separate the equation into 2 possible cases

x^{3} = 0 21 x^{3} - 5 = 0

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

x = 0 21 x^{3} - 5 = 0

Solve the equation

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Evaluate

21 x^{3} - 5 = 0

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

21 x^{3} = 0 + 5

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

21 x^{3} = 5

Divide both sides

\frac{21 x ^{3}}{21} = \frac{5}{21}

Divide the numbers

x^{3} = \frac{5}{21}

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

3 x^{3} = 3 \frac{5}{21}

Calculate

x = 3 \frac{5}{21}

Simplify the root

More Steps

Evaluate

3 \frac{5}{21}

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

\frac{3 5}{3 21}

Multiply by the Conjugate

\frac{3 5 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{3 5 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

\frac{3 2205}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

\frac{3 2205}{21}

x = \frac{3 2205}{21}

x = 0 x = \frac{3 2205}{21}

Solution

x_{1} = 0, x_{2} = \frac{3 2205}{21}

Alternative Form

x_{1} = 0, x_{2} \approx 0.619798

Show Solution