Solve -2x^2 5x-4=0

Question

Solve the equation

x = - \frac{3 50}{5}

Alternative Form

x \approx - 0.736806

Evaluate

- 2 x^{2} \times 5 x - 4 = 0

Multiply

More Steps

Evaluate

- 2 x^{2} \times 5 x

Multiply the terms

- 10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 10 x^{2 + 1}

Add the numbers

- 10 x^{3}

- 10 x^{3} - 4 = 0

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

- 10 x^{3} = 0 + 4

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

- 10 x^{3} = 4

Change the signs on both sides of the equation

10 x^{3} = - 4

Divide both sides

\frac{10 x ^{3}}{10} = \frac{- 4}{10}

Divide the numbers

x^{3} = \frac{- 4}{10}

Divide the numbers

More Steps

Evaluate

\frac{- 4}{10}

Cancel out the common factor 2

\frac{- 2}{5}

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

- \frac{2}{5}

x^{3} = - \frac{2}{5}

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

3 x^{3} = 3 - \frac{2}{5}

Calculate

x = 3 - \frac{2}{5}

Solution

More Steps

Evaluate

3 - \frac{2}{5}

An odd root of a negative radicand is always a negative

- 3 \frac{2}{5}

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

- \frac{3 2}{3 5}

Multiply by the Conjugate

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

Simplify

\frac{- 3 2 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 32 \times 325

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

- 3 2 \times 25

Calculate the product

- 350

\frac{- 3 50}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{- 3 50}{5}

Calculate

- \frac{3 50}{5}

x = - \frac{3 50}{5}

Alternative Form

x \approx - 0.736806

Show Solution