Solve -2x^4 2x^2 2 7x^4 - 2x

Question

Simplify the expression

- 108 x^{10} - 2 x

Evaluate

- 2 x^{4} \times 2 x^{2} \times 27 x^{4} - 2 x

Solution

More Steps

Evaluate

- 2 x^{4} \times 2 x^{2} \times 27 x^{4}

Multiply the terms

More Steps

Evaluate

2 \times 2 \times 27

Multiply the terms

4 \times 27

Multiply the numbers

108

- 108 x^{4} \times x^{2} \times x^{4}

Multiply the terms with the same base by adding their exponents

- 108 x^{4 + 2 + 4}

Add the numbers

- 108 x^{10}

- 108 x^{10} - 2 x

Show Solution

Factor the expression

- 2 x (54 x^{9} + 1)

Evaluate

- 2 x^{4} \times 2 x^{2} \times 27 x^{4} - 2 x

Multiply

More Steps

Evaluate

- 2 x^{4} \times 2 x^{2} \times 27 x^{4}

Multiply the terms

More Steps

Evaluate

2 \times 2 \times 27

Multiply the terms

4 \times 27

Multiply the numbers

108

- 108 x^{4} \times x^{2} \times x^{4}

Multiply the terms with the same base by adding their exponents

- 108 x^{4 + 2 + 4}

Add the numbers

- 108 x^{10}

- 108 x^{10} - 2 x

Rewrite the expression

- 2 x \times 54 x^{9} - 2 x

Solution

- 2 x (54 x^{9} + 1)

Show Solution

Find the roots

x_{1} = - \frac{9 5 4 ^{8}}{54}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.641966, x_{2} = 0

Evaluate

- 2 x^{4} \times 2 x^{2} \times 27 x^{4} - 2 x

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

- 2 x^{4} \times 2 x^{2} \times 27 x^{4} - 2 x = 0

Multiply

More Steps

Multiply the terms

- 2 x^{4} \times 2 x^{2} \times 27 x^{4}

Multiply the terms

More Steps

Evaluate

2 \times 2 \times 27

Multiply the terms

4 \times 27

Multiply the numbers

108

- 108 x^{4} \times x^{2} \times x^{4}

Multiply the terms with the same base by adding their exponents

- 108 x^{4 + 2 + 4}

Add the numbers

- 108 x^{10}

- 108 x^{10} - 2 x = 0

Factor the expression

- 2 x (54 x^{9} + 1) = 0

Divide both sides

x (54 x^{9} + 1) = 0

Separate the equation into 2 possible cases

x = 0 54 x^{9} + 1 = 0

Solve the equation

More Steps

Evaluate

54 x^{9} + 1 = 0

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

54 x^{9} = 0 - 1

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

54 x^{9} = - 1

Divide both sides

\frac{54 x ^{9}}{54} = \frac{- 1}{54}

Divide the numbers

x^{9} = \frac{- 1}{54}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{9} = - \frac{1}{54}

Take the 9 -th root on both sides of the equation

9 x^{9} = 9 - \frac{1}{54}

Calculate

x = 9 - \frac{1}{54}

Simplify the root

More Steps

Evaluate

9 - \frac{1}{54}

An odd root of a negative radicand is always a negative

- 9 \frac{1}{54}

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

- \frac{9 1}{9 54}

Simplify the radical expression

- \frac{1}{9 54}

Multiply by the Conjugate

\frac{- 9 5 4 ^{8}}{9 54 \times 9 5 4 ^{8}}

Multiply the numbers

\frac{- 9 5 4 ^{8}}{54}

Calculate

- \frac{9 5 4 ^{8}}{54}

x = - \frac{9 5 4 ^{8}}{54}

x = 0 x = - \frac{9 5 4 ^{8}}{54}

Solution

x_{1} = - \frac{9 5 4 ^{8}}{54}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.641966, x_{2} = 0

Show Solution