Solve -3x^2 17x-20

Question

Simplify the expression

- 51 x^{3} - 20

Evaluate

- 3 x^{2} \times 17 x - 20

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} - 20

Show Solution

x = - \frac{3 52020}{51}

Alternative Form

x \approx - 0.731959

Evaluate

- 3 x^{2} \times 17 x - 20

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

- 3 x^{2} \times 17 x - 20 = 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} - 20 = 0

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

- 51 x^{3} = 0 + 20

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

- 51 x^{3} = 20

Change the signs on both sides of the equation

51 x^{3} = - 20

Divide both sides

\frac{51 x ^{3}}{51} = \frac{- 20}{51}

Divide the numbers

x^{3} = \frac{- 20}{51}

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

x^{3} = - \frac{20}{51}

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

3 x^{3} = 3 - \frac{20}{51}

Calculate

x = 3 - \frac{20}{51}

Solution

More Steps

Evaluate

3 - \frac{20}{51}

An odd root of a negative radicand is always a negative

- 3 \frac{20}{51}

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

- \frac{3 20}{3 51}

Multiply by the Conjugate

\frac{- 3 20 \times 3 5 1 ^{2}}{3 51 \times 3 5 1 ^{2}}

Simplify

\frac{- 3 20 \times 3 2601}{3 51 \times 3 5 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 320 \times 32601

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

- 3 20 \times 2601

Calculate the product

- 352020

\frac{- 3 52020}{3 51 \times 3 5 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

351 \times 3 5 1^{2}

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

3 51 \times 5 1^{2}

Calculate the product

3 5 1^{3}

Reduce the index of the radical and exponent with 3

51

\frac{- 3 52020}{51}

Calculate

- \frac{3 52020}{51}

x = - \frac{3 52020}{51}

Alternative Form

x \approx - 0.731959

Show Solution