Solve 3x^3 12x^2 3x-18

Question

Simplify the expression

108 x^{6} - 18

Evaluate

3 x^{3} \times 12 x^{2} \times 3 x - 18

Solution

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Evaluate

3 x^{3} \times 12 x^{2} \times 3 x

Multiply the terms

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Evaluate

3 \times 12 \times 3

Multiply the terms

36 \times 3

Multiply the numbers

108

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

Multiply the terms with the same base by adding their exponents

108 x^{3 + 2 + 1}

Add the numbers

108 x^{6}

108 x^{6} - 18

Show Solution

Factor the expression

18 (6 x^{6} - 1)

Evaluate

3 x^{3} \times 12 x^{2} \times 3 x - 18

Multiply

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Evaluate

3 x^{3} \times 12 x^{2} \times 3 x

Multiply the terms

More Steps

Evaluate

3 \times 12 \times 3

Multiply the terms

36 \times 3

Multiply the numbers

108

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

Multiply the terms with the same base by adding their exponents

108 x^{3 + 2 + 1}

Add the numbers

108 x^{6}

108 x^{6} - 18

Solution

18 (6 x^{6} - 1)

Show Solution

Find the roots

x_{1} = - \frac{6 7776}{6}, x_{2} = \frac{6 7776}{6}

Alternative Form

x_{1} \approx - 0.741836, x_{2} \approx 0.741836

Evaluate

3 x^{3} \times 12 x^{2} \times 3 x - 18

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

3 x^{3} \times 12 x^{2} \times 3 x - 18 = 0

Multiply

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Multiply the terms

3 x^{3} \times 12 x^{2} \times 3 x

Multiply the terms

More Steps

Evaluate

3 \times 12 \times 3

Multiply the terms

36 \times 3

Multiply the numbers

108

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

Multiply the terms with the same base by adding their exponents

108 x^{3 + 2 + 1}

Add the numbers

108 x^{6}

108 x^{6} - 18 = 0

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

108 x^{6} = 0 + 18

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

108 x^{6} = 18

Divide both sides

\frac{108 x ^{6}}{108} = \frac{18}{108}

Divide the numbers

x^{6} = \frac{18}{108}

Cancel out the common factor 18

x^{6} = \frac{1}{6}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 6 \frac{1}{6}

Simplify the expression

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Evaluate

6 \frac{1}{6}

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

\frac{6 1}{6 6}

Simplify the radical expression

\frac{1}{6 6}

Multiply by the Conjugate

\frac{6 6 ^{5}}{6 6 \times 6 6 ^{5}}

Simplify

\frac{6 7776}{6 6 \times 6 6 ^{5}}

Multiply the numbers

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Evaluate

66 \times 6 6^{5}

The product of roots with the same index is equal to the root of the product

6 6 \times 6^{5}

Calculate the product

6 6^{6}

Reduce the index of the radical and exponent with 6

6

\frac{6 7776}{6}

x = \pm \frac{6 7776}{6}

Separate the equation into 2 possible cases

x = \frac{6 7776}{6} x = - \frac{6 7776}{6}

Solution

x_{1} = - \frac{6 7776}{6}, x_{2} = \frac{6 7776}{6}

Alternative Form

x_{1} \approx - 0.741836, x_{2} \approx 0.741836

Show Solution