Solve - 5x^26x-2=0

Question

Solve the equation

x = - \frac{3 225}{15}

Alternative Form

x \approx - 0.40548

Evaluate

- 5 x^{2} \times 6 x - 2 = 0

Multiply

More Steps

Evaluate

- 5 x^{2} \times 6 x

Multiply the terms

- 30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 30 x^{2 + 1}

Add the numbers

- 30 x^{3}

- 30 x^{3} - 2 = 0

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

- 30 x^{3} = 0 + 2

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

- 30 x^{3} = 2

Change the signs on both sides of the equation

30 x^{3} = - 2

Divide both sides

\frac{30 x ^{3}}{30} = \frac{- 2}{30}

Divide the numbers

x^{3} = \frac{- 2}{30}

Divide the numbers

More Steps

Evaluate

\frac{- 2}{30}

Cancel out the common factor 2

\frac{- 1}{15}

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

- \frac{1}{15}

x^{3} = - \frac{1}{15}

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

3 x^{3} = 3 - \frac{1}{15}

Calculate

x = 3 - \frac{1}{15}

Solution

More Steps

Evaluate

3 - \frac{1}{15}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{15}

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

- \frac{3 1}{3 15}

Simplify the radical expression

- \frac{1}{3 15}

Multiply by the Conjugate

\frac{- 3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{- 3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3 1 5^{2}

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

3 15 \times 1 5^{2}

Calculate the product

3 1 5^{3}

Reduce the index of the radical and exponent with 3

15

\frac{- 3 225}{15}

Calculate

- \frac{3 225}{15}

x = - \frac{3 225}{15}

Alternative Form

x \approx - 0.40548

Show Solution