Solve -3x^217x-24

Question

Simplify the expression

- 51 x^{3} - 24

Evaluate

- 3 x^{2} \times 17 x - 24

Solution

More Steps

Evaluate

- 3 x^{2} \times 17 x

Multiply the terms

- 51 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 51 x^{2 + 1}

Add the numbers

- 51 x^{3}

- 51 x^{3} - 24

Show Solution

Factor the expression

- 3 (17 x^{3} + 8)

Evaluate

- 3 x^{2} \times 17 x - 24

Multiply

More Steps

Evaluate

- 3 x^{2} \times 17 x

Multiply the terms

- 51 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 51 x^{2 + 1}

Add the numbers

- 51 x^{3}

- 51 x^{3} - 24

Solution

- 3 (17 x^{3} + 8)

Show Solution

Find the roots

x = - \frac{2 3 289}{17}

Alternative Form

x \approx - 0.777822

Evaluate

- 3 x^{2} \times 17 x - 24

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

- 3 x^{2} \times 17 x - 24 = 0

Multiply

More Steps

Multiply the terms

- 3 x^{2} \times 17 x

Multiply the terms

- 51 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 51 x^{2 + 1}

Add the numbers

- 51 x^{3}

- 51 x^{3} - 24 = 0

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

- 51 x^{3} = 0 + 24

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

- 51 x^{3} = 24

Change the signs on both sides of the equation

51 x^{3} = - 24

Divide both sides

\frac{51 x ^{3}}{51} = \frac{- 24}{51}

Divide the numbers

x^{3} = \frac{- 24}{51}

Divide the numbers

More Steps

Evaluate

\frac{- 24}{51}

Cancel out the common factor 3

\frac{- 8}{17}

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

- \frac{8}{17}

x^{3} = - \frac{8}{17}

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

3 x^{3} = 3 - \frac{8}{17}

Calculate

x = 3 - \frac{8}{17}

Solution

More Steps

Evaluate

3 - \frac{8}{17}

An odd root of a negative radicand is always a negative

- 3 \frac{8}{17}

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

- \frac{3 8}{3 17}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

- \frac{2}{3 17}

Multiply by the Conjugate

\frac{- 2 3 1 7 ^{2}}{3 17 \times 3 1 7 ^{2}}

Simplify

\frac{- 2 3 289}{3 17 \times 3 1 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

317 \times 3 1 7^{2}

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

3 17 \times 1 7^{2}

Calculate the product

3 1 7^{3}

Reduce the index of the radical and exponent with 3

17

\frac{- 2 3 289}{17}

Calculate

- \frac{2 3 289}{17}

x = - \frac{2 3 289}{17}

Alternative Form

x \approx - 0.777822

Show Solution