Solve 4 - 5(-4n^3)

Question

Simplify the expression

4 + 20 n^{3}

Evaluate

4 - 5 (- 4 n^{3})

Multiply the numbers

More Steps

Evaluate

5 (- 4)

Multiplying or dividing an odd number of negative terms equals a negative

- 5 \times 4

Multiply the numbers

- 20

4 - (- 20 n^{3})

Solution

4 + 20 n^{3}

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Factor the expression

4 (1 + 5 n^{3})

Evaluate

4 - 5 (- 4 n^{3})

Multiply the numbers

More Steps

Evaluate

5 (- 4)

Multiplying or dividing an odd number of negative terms equals a negative

- 5 \times 4

Multiply the numbers

- 20

Evaluate

- 20 n^{3}

4 - (- 20 n^{3})

Rewrite the expression

4 + 20 n^{3}

Solution

4 (1 + 5 n^{3})

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Find the roots

n = - \frac{3 25}{5}

Alternative Form

n \approx - 0.584804

Evaluate

4 - 5 (- 4 n^{3})

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

4 - 5 (- 4 n^{3}) = 0

Multiply the numbers

More Steps

Evaluate

5 (- 4)

Multiplying or dividing an odd number of negative terms equals a negative

- 5 \times 4

Multiply the numbers

- 20

4 - (- 20 n^{3}) = 0

Rewrite the expression

4 + 20 n^{3} = 0

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

20 n^{3} = 0 - 4

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

20 n^{3} = - 4

Divide both sides

\frac{20 n ^{3}}{20} = \frac{- 4}{20}

Divide the numbers

n^{3} = \frac{- 4}{20}

Divide the numbers

More Steps

Evaluate

\frac{- 4}{20}

Cancel out the common factor 4

\frac{- 1}{5}

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

- \frac{1}{5}

n^{3} = - \frac{1}{5}

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

3 n^{3} = 3 - \frac{1}{5}

Calculate

n = 3 - \frac{1}{5}

Solution

More Steps

Evaluate

3 - \frac{1}{5}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{5}

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

- \frac{3 1}{3 5}

Simplify the radical expression

- \frac{1}{3 5}

Multiply by the Conjugate

\frac{- 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{- 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{- 3 25}{5}

Calculate

- \frac{3 25}{5}

n = - \frac{3 25}{5}

Alternative Form

n \approx - 0.584804

Show Solution