Solve -6n^(2) 41n-70

Question

Simplify the expression

- 246 n^{3} - 70

Evaluate

- 6 n^{2} \times 41 n - 70

Solution

More Steps

Evaluate

- 6 n^{2} \times 41 n

Multiply the terms

- 246 n^{2} \times n

Multiply the terms with the same base by adding their exponents

- 246 n^{2 + 1}

Add the numbers

- 246 n^{3}

- 246 n^{3} - 70

Show Solution

Factor the expression

- 2 (123 n^{3} + 35)

Evaluate

- 6 n^{2} \times 41 n - 70

Multiply

More Steps

Evaluate

- 6 n^{2} \times 41 n

Multiply the terms

- 246 n^{2} \times n

Multiply the terms with the same base by adding their exponents

- 246 n^{2 + 1}

Add the numbers

- 246 n^{3}

- 246 n^{3} - 70

Solution

- 2 (123 n^{3} + 35)

Show Solution

Find the roots

n = - \frac{3 529515}{123}

Alternative Form

n \approx - 0.65774

Evaluate

- 6 n^{2} \times 41 n - 70

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

- 6 n^{2} \times 41 n - 70 = 0

Multiply

More Steps

Multiply the terms

- 6 n^{2} \times 41 n

Multiply the terms

- 246 n^{2} \times n

Multiply the terms with the same base by adding their exponents

- 246 n^{2 + 1}

Add the numbers

- 246 n^{3}

- 246 n^{3} - 70 = 0

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

- 246 n^{3} = 0 + 70

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

- 246 n^{3} = 70

Change the signs on both sides of the equation

246 n^{3} = - 70

Divide both sides

\frac{246 n ^{3}}{246} = \frac{- 70}{246}

Divide the numbers

n^{3} = \frac{- 70}{246}

Divide the numbers

More Steps

Evaluate

\frac{- 70}{246}

Cancel out the common factor 2

\frac{- 35}{123}

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

- \frac{35}{123}

n^{3} = - \frac{35}{123}

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

3 n^{3} = 3 - \frac{35}{123}

Calculate

n = 3 - \frac{35}{123}

Solution

More Steps

Evaluate

3 - \frac{35}{123}

An odd root of a negative radicand is always a negative

- 3 \frac{35}{123}

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

- \frac{3 35}{3 123}

Multiply by the Conjugate

\frac{- 3 35 \times 3 12 3 ^{2}}{3 123 \times 3 12 3 ^{2}}

Simplify

\frac{- 3 35 \times 3 15129}{3 123 \times 3 12 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 335 \times 315129

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

- 3 35 \times 15129

Calculate the product

- 3529515

\frac{- 3 529515}{3 123 \times 3 12 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

3123 \times 3 12 3^{2}

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

3 123 \times 12 3^{2}

Calculate the product

3 12 3^{3}

Reduce the index of the radical and exponent with 3

123

\frac{- 3 529515}{123}

Calculate

- \frac{3 529515}{123}

n = - \frac{3 529515}{123}

Alternative Form

n \approx - 0.65774

Show Solution