Solve 3x^3-7x^2 6x-14 0

Question

Simplify the expression

- 39 x^{3} - 140

Evaluate

3 x^{3} - 7 x^{2} \times 6 x - 140

Multiply

More Steps

Multiply the terms

- 7 x^{2} \times 6 x

Multiply the terms

- 42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 42 x^{2 + 1}

Add the numbers

- 42 x^{3}

3 x^{3} - 42 x^{3} - 140

Solution

More Steps

Evaluate

3 x^{3} - 42 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(3 - 42) x^{3}

Subtract the numbers

- 39 x^{3}

- 39 x^{3} - 140

Show Solution

Find the roots

x = - \frac{3 212940}{39}

Alternative Form

x \approx - 1.531162

Evaluate

3 x^{3} - 7 x^{2} \times 6 x - 140

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

3 x^{3} - 7 x^{2} \times 6 x - 140 = 0

Multiply

More Steps

Multiply the terms

7 x^{2} \times 6 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

3 x^{3} - 42 x^{3} - 140 = 0

Subtract the terms

More Steps

Simplify

3 x^{3} - 42 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(3 - 42) x^{3}

Subtract the numbers

- 39 x^{3}

- 39 x^{3} - 140 = 0

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

- 39 x^{3} = 0 + 140

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

- 39 x^{3} = 140

Change the signs on both sides of the equation

39 x^{3} = - 140

Divide both sides

\frac{39 x ^{3}}{39} = \frac{- 140}{39}

Divide the numbers

x^{3} = \frac{- 140}{39}

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

x^{3} = - \frac{140}{39}

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

3 x^{3} = 3 - \frac{140}{39}

Calculate

x = 3 - \frac{140}{39}

Solution

More Steps

Evaluate

3 - \frac{140}{39}

An odd root of a negative radicand is always a negative

- 3 \frac{140}{39}

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

- \frac{3 140}{3 39}

Multiply by the Conjugate

\frac{- 3 140 \times 3 3 9 ^{2}}{3 39 \times 3 3 9 ^{2}}

Simplify

\frac{- 3 140 \times 3 1521}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 3140 \times 31521

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

- 3 140 \times 1521

Calculate the product

- 3212940

\frac{- 3 212940}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

339 \times 3 3 9^{2}

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

3 39 \times 3 9^{2}

Calculate the product

3 3 9^{3}

Reduce the index of the radical and exponent with 3

39

\frac{- 3 212940}{39}

Calculate

- \frac{3 212940}{39}

x = - \frac{3 212940}{39}

Alternative Form

x \approx - 1.531162

Show Solution