Solve (-2x-1)(x^29x^3)

Question

Simplify the expression

- 18 x^{6} - 9 x^{5}

Evaluate

(- 2 x - 1) (x^{2} \times 9 x^{3})

Remove the parentheses

(- 2 x - 1) x^{2} \times 9 x^{3}

Multiply the terms with the same base by adding their exponents

(- 2 x - 1) x^{2 + 3} \times 9

Add the numbers

(- 2 x - 1) x^{5} \times 9

Use the commutative property to reorder the terms

(- 2 x - 1) \times 9 x^{5}

Multiply the terms

9 x^{5} (- 2 x - 1)

Apply the distributive property

9 x^{5} (- 2 x) - 9 x^{5} \times 1

Multiply the terms

More Steps

Evaluate

9 x^{5} (- 2 x)

Multiply the numbers

More Steps

Evaluate

9 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 9 \times 2

Multiply the numbers

- 18

- 18 x^{5} \times x

Multiply the terms

More Steps

Evaluate

x^{5} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{5 + 1}

Add the numbers

x^{6}

- 18 x^{6}

- 18 x^{6} - 9 x^{5} \times 1

Solution

- 18 x^{6} - 9 x^{5}

Show Solution

x_{1} = - \frac{1}{2}, x_{2} = 0

Alternative Form

x_{1} = - 0.5, x_{2} = 0

Evaluate

(- 2 x - 1) (x^{2} \times 9 x^{3})

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

(- 2 x - 1) (x^{2} \times 9 x^{3}) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 9 x^{3}

Multiply the terms with the same base by adding their exponents

x^{2 + 3} \times 9

Add the numbers

x^{5} \times 9

Use the commutative property to reorder the terms

9 x^{5}

(- 2 x - 1) \times 9 x^{5} = 0

Multiply the terms

9 x^{5} (- 2 x - 1) = 0

Elimination the left coefficient

x^{5} (- 2 x - 1) = 0

Separate the equation into 2 possible cases

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

The only way a power can be 0 is when the base equals 0

x = 0 - 2 x - 1 = 0

Solve the equation

More Steps

Evaluate

- 2 x - 1 = 0

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

- 2 x = 0 + 1

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

- 2 x = 1

Change the signs on both sides of the equation

2 x = - 1

Divide both sides

\frac{2 x}{2} = \frac{- 1}{2}

Divide the numbers

x = \frac{- 1}{2}

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

x = - \frac{1}{2}

x = 0 x = - \frac{1}{2}

Solution

x_{1} = - \frac{1}{2}, x_{2} = 0

Alternative Form

x_{1} = - 0.5, x_{2} = 0

Show Solution