Solve -x^2 5x -1 = 0

Question

Solve the equation

x = - \frac{3 25}{5}

Alternative Form

x \approx - 0.584804

Evaluate

- x^{2} \times 5 x - 1 = 0

Multiply

More Steps

Evaluate

- x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 5

Add the numbers

- x^{3} \times 5

Use the commutative property to reorder the terms

- 5 x^{3}

- 5 x^{3} - 1 = 0

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

- 5 x^{3} = 0 + 1

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

- 5 x^{3} = 1

Change the signs on both sides of the equation

5 x^{3} = - 1

Divide both sides

\frac{5 x ^{3}}{5} = \frac{- 1}{5}

Divide the numbers

x^{3} = \frac{- 1}{5}

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

x^{3} = - \frac{1}{5}

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

3 x^{3} = 3 - \frac{1}{5}

Calculate

x = 3 - \frac{1}{5}

Solution

More Steps

Evaluate

3 - \frac{1}{5}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{5}

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

- \frac{3 1}{3 5}

Simplify the radical expression

- \frac{1}{3 5}

Multiply by the Conjugate

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

Simplify

\frac{- 3 25}{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 25}{5}

Calculate

- \frac{3 25}{5}

x = - \frac{3 25}{5}

Alternative Form

x \approx - 0.584804

Show Solution