Solve 9x^2(3x^2 14x-8)

Question

Simplify the expression

378 x^{5} - 72 x^{2}

Evaluate

9 x^{2} (3 x^{2} \times 14 x - 8)

Multiply

More Steps

Evaluate

3 x^{2} \times 14 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

9 x^{2} (42 x^{3} - 8)

Apply the distributive property

9 x^{2} \times 42 x^{3} - 9 x^{2} \times 8

Multiply the terms

More Steps

Evaluate

9 x^{2} \times 42 x^{3}

Multiply the numbers

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

Multiply the terms

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Evaluate

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

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

x^{2 + 3}

Add the numbers

x^{5}

378 x^{5}

378 x^{5} - 9 x^{2} \times 8

Solution

378 x^{5} - 72 x^{2}

Show Solution

Factor the expression

18 x^{2} (21 x^{3} - 4)

Evaluate

9 x^{2} (3 x^{2} \times 14 x - 8)

Multiply

More Steps

Evaluate

3 x^{2} \times 14 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

9 x^{2} (42 x^{3} - 8)

Factor the expression

9 x^{2} \times 2 (21 x^{3} - 4)

Solution

18 x^{2} (21 x^{3} - 4)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 1764}{21}

Alternative Form

x_{1} = 0, x_{2} \approx 0.57537

Evaluate

9 x^{2} (3 x^{2} \times 14 x - 8)

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

9 x^{2} (3 x^{2} \times 14 x - 8) = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 14 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

9 x^{2} (42 x^{3} - 8) = 0

Elimination the left coefficient

x^{2} (42 x^{3} - 8) = 0

Separate the equation into 2 possible cases

x^{2} = 0 42 x^{3} - 8 = 0

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

x = 0 42 x^{3} - 8 = 0

Solve the equation

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Evaluate

42 x^{3} - 8 = 0

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

42 x^{3} = 0 + 8

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

42 x^{3} = 8

Divide both sides

\frac{42 x ^{3}}{42} = \frac{8}{42}

Divide the numbers

x^{3} = \frac{8}{42}

Cancel out the common factor 2

x^{3} = \frac{4}{21}

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

3 x^{3} = 3 \frac{4}{21}

Calculate

x = 3 \frac{4}{21}

Simplify the root

More Steps

Evaluate

3 \frac{4}{21}

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

\frac{3 4}{3 21}

Multiply by the Conjugate

\frac{3 4 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{3 4 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

\frac{3 1764}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

\frac{3 1764}{21}

x = \frac{3 1764}{21}

x = 0 x = \frac{3 1764}{21}

Solution

x_{1} = 0, x_{2} = \frac{3 1764}{21}

Alternative Form

x_{1} = 0, x_{2} \approx 0.57537

Show Solution