Solve a^3-3a^2 5a-17

Question

Simplify the expression

- 14 a^{3} - 17

Evaluate

a^{3} - 3 a^{2} \times 5 a - 17

Multiply

More Steps

Multiply the terms

- 3 a^{2} \times 5 a

Multiply the terms

- 15 a^{2} \times a

Multiply the terms with the same base by adding their exponents

- 15 a^{2 + 1}

Add the numbers

- 15 a^{3}

a^{3} - 15 a^{3} - 17

Solution

More Steps

Evaluate

a^{3} - 15 a^{3}

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

(1 - 15) a^{3}

Subtract the numbers

- 14 a^{3}

- 14 a^{3} - 17

Show Solution

Find the roots

a = - \frac{3 3332}{14}

Alternative Form

a \approx - 1.066859

Evaluate

a^{3} - 3 a^{2} \times 5 a - 17

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

a^{3} - 3 a^{2} \times 5 a - 17 = 0

Multiply

More Steps

Multiply the terms

3 a^{2} \times 5 a

Multiply the terms

15 a^{2} \times a

Multiply the terms with the same base by adding their exponents

15 a^{2 + 1}

Add the numbers

15 a^{3}

a^{3} - 15 a^{3} - 17 = 0

Subtract the terms

More Steps

Simplify

a^{3} - 15 a^{3}

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

(1 - 15) a^{3}

Subtract the numbers

- 14 a^{3}

- 14 a^{3} - 17 = 0

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

- 14 a^{3} = 0 + 17

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

- 14 a^{3} = 17

Change the signs on both sides of the equation

14 a^{3} = - 17

Divide both sides

\frac{14 a ^{3}}{14} = \frac{- 17}{14}

Divide the numbers

a^{3} = \frac{- 17}{14}

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

a^{3} = - \frac{17}{14}

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

3 a^{3} = 3 - \frac{17}{14}

Calculate

a = 3 - \frac{17}{14}

Solution

More Steps

Evaluate

3 - \frac{17}{14}

An odd root of a negative radicand is always a negative

- 3 \frac{17}{14}

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

- \frac{3 17}{3 14}

Multiply by the Conjugate

\frac{- 3 17 \times 3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{- 3 17 \times 3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 317 \times 3196

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

- 3 17 \times 196

Calculate the product

- 33332

\frac{- 3 3332}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 3 1 4^{2}

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

3 14 \times 1 4^{2}

Calculate the product

3 1 4^{3}

Reduce the index of the radical and exponent with 3

14

\frac{- 3 3332}{14}

Calculate

- \frac{3 3332}{14}

a = - \frac{3 3332}{14}

Alternative Form

a \approx - 1.066859

Show Solution