Solve 18x^3 81x-27

Question

Simplify the expression

1458 x^{4} - 27

Evaluate

18 x^{3} \times 81 x - 27

Solution

More Steps

Evaluate

18 x^{3} \times 81 x

Multiply the terms

1458 x^{3} \times x

Multiply the terms with the same base by adding their exponents

1458 x^{3 + 1}

Add the numbers

1458 x^{4}

1458 x^{4} - 27

Show Solution

Factor the expression

27 (54 x^{4} - 1)

Evaluate

18 x^{3} \times 81 x - 27

Multiply

More Steps

Evaluate

18 x^{3} \times 81 x

Multiply the terms

1458 x^{3} \times x

Multiply the terms with the same base by adding their exponents

1458 x^{3 + 1}

Add the numbers

1458 x^{4}

1458 x^{4} - 27

Solution

27 (54 x^{4} - 1)

Show Solution

Find the roots

x_{1} = - \frac{4 5 4 ^{3}}{54}, x_{2} = \frac{4 5 4 ^{3}}{54}

Alternative Form

x_{1} \approx - 0.368894, x_{2} \approx 0.368894

Evaluate

18 x^{3} \times 81 x - 27

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

18 x^{3} \times 81 x - 27 = 0

Multiply

More Steps

Multiply the terms

18 x^{3} \times 81 x

Multiply the terms

1458 x^{3} \times x

Multiply the terms with the same base by adding their exponents

1458 x^{3 + 1}

Add the numbers

1458 x^{4}

1458 x^{4} - 27 = 0

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

1458 x^{4} = 0 + 27

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

1458 x^{4} = 27

Divide both sides

\frac{1458 x ^{4}}{1458} = \frac{27}{1458}

Divide the numbers

x^{4} = \frac{27}{1458}

Cancel out the common factor 27

x^{4} = \frac{1}{54}

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

x = \pm 4 \frac{1}{54}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{54}

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

\frac{4 1}{4 54}

Simplify the radical expression

\frac{1}{4 54}

Multiply by the Conjugate

\frac{4 5 4 ^{3}}{4 54 \times 4 5 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

454 \times 4 5 4^{3}

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

4 54 \times 5 4^{3}

Calculate the product

4 5 4^{4}

Reduce the index of the radical and exponent with 4

54

\frac{4 5 4 ^{3}}{54}

x = \pm \frac{4 5 4 ^{3}}{54}

Separate the equation into 2 possible cases

x = \frac{4 5 4 ^{3}}{54} x = - \frac{4 5 4 ^{3}}{54}

Solution

x_{1} = - \frac{4 5 4 ^{3}}{54}, x_{2} = \frac{4 5 4 ^{3}}{54}

Alternative Form

x_{1} \approx - 0.368894, x_{2} \approx 0.368894

Show Solution