Solve -x^2 6x-10=0

Question

Solve the equation

x = - \frac{3 45}{3}

Alternative Form

x \approx - 1.185631

Evaluate

- x^{2} \times 6 x - 10 = 0

Multiply

More Steps

Evaluate

- x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 6

Add the numbers

- x^{3} \times 6

Use the commutative property to reorder the terms

- 6 x^{3}

- 6 x^{3} - 10 = 0

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

- 6 x^{3} = 0 + 10

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

- 6 x^{3} = 10

Change the signs on both sides of the equation

6 x^{3} = - 10

Divide both sides

\frac{6 x ^{3}}{6} = \frac{- 10}{6}

Divide the numbers

x^{3} = \frac{- 10}{6}

Divide the numbers

More Steps

Evaluate

\frac{- 10}{6}

Cancel out the common factor 2

\frac{- 5}{3}

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

- \frac{5}{3}

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

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

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

Calculate

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

Solution

More Steps

Evaluate

3 - \frac{5}{3}

An odd root of a negative radicand is always a negative

- 3 \frac{5}{3}

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

- \frac{3 5}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{- 3 5 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 35 \times 39

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

- 3 5 \times 9

Calculate the product

- 345

\frac{- 3 45}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{- 3 45}{3}

Calculate

- \frac{3 45}{3}

x = - \frac{3 45}{3}

Alternative Form

x \approx - 1.185631

Show Solution