Solve -c^3 2c^2 - c^29/27

Question

Simplify the expression

- 2 c^{5} - \frac{1}{3} c^{2}

Evaluate

- c^{3} \times 2 c^{2} - c^{2} \times \frac{9}{27}

Cancel out the common factor 9

- c^{3} \times 2 c^{2} - c^{2} \times \frac{1}{3}

Multiply

More Steps

Multiply the terms

- c^{3} \times 2 c^{2}

Multiply the terms with the same base by adding their exponents

- c^{3 + 2} \times 2

Add the numbers

- c^{5} \times 2

Use the commutative property to reorder the terms

- 2 c^{5}

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

Solution

- 2 c^{5} - \frac{1}{3} c^{2}

Show Solution

Factor the expression

- \frac{1}{3} c^{2} (6 c^{3} + 1)

Evaluate

- c^{3} \times 2 c^{2} - c^{2} \times \frac{9}{27}

Multiply

More Steps

Multiply the terms

c^{3} \times 2 c^{2}

Multiply the terms with the same base by adding their exponents

c^{3 + 2} \times 2

Add the numbers

c^{5} \times 2

Use the commutative property to reorder the terms

2 c^{5}

- 2 c^{5} - c^{2} \times \frac{9}{27}

Cancel out the common factor 9

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

Use the commutative property to reorder the terms

- 2 c^{5} - \frac{1}{3} c^{2}

Rewrite the expression

- \frac{1}{3} c^{2} \times 6 c^{3} - \frac{1}{3} c^{2}

Solution

- \frac{1}{3} c^{2} (6 c^{3} + 1)

Show Solution

Find the roots

c_{1} = - \frac{3 36}{6}, c_{2} = 0

Alternative Form

c_{1} \approx - 0.550321, c_{2} = 0

Evaluate

- c^{3} \times 2 c^{2} - c^{2} \times \frac{9}{27}

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

- c^{3} \times 2 c^{2} - c^{2} \times \frac{9}{27} = 0

Multiply

More Steps

Multiply the terms

c^{3} \times 2 c^{2}

Multiply the terms with the same base by adding their exponents

c^{3 + 2} \times 2

Add the numbers

c^{5} \times 2

Use the commutative property to reorder the terms

2 c^{5}

- 2 c^{5} - c^{2} \times \frac{9}{27} = 0

Cancel out the common factor 9

- 2 c^{5} - c^{2} \times \frac{1}{3} = 0

Use the commutative property to reorder the terms

- 2 c^{5} - \frac{1}{3} c^{2} = 0

Factor the expression

c^{2} (- 2 c^{3} - \frac{1}{3}) = 0

Separate the equation into 2 possible cases

c^{2} = 0 - 2 c^{3} - \frac{1}{3} = 0

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

c = 0 - 2 c^{3} - \frac{1}{3} = 0

Solve the equation

More Steps

Evaluate

- 2 c^{3} - \frac{1}{3} = 0

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

- 2 c^{3} = 0 + \frac{1}{3}

Add the terms

- 2 c^{3} = \frac{1}{3}

Change the signs on both sides of the equation

2 c^{3} = - \frac{1}{3}

Multiply by the reciprocal

2 c^{3} \times \frac{1}{2} = - \frac{1}{3} \times \frac{1}{2}

Multiply

c^{3} = - \frac{1}{3} \times \frac{1}{2}

Multiply

More Steps

Evaluate

- \frac{1}{3} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{1}{3 \times 2}

Multiply the numbers

- \frac{1}{6}

c^{3} = - \frac{1}{6}

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

3 c^{3} = 3 - \frac{1}{6}

Calculate

c = 3 - \frac{1}{6}

Simplify the root

More Steps

Evaluate

3 - \frac{1}{6}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{6}

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

- \frac{3 1}{3 6}

Simplify the radical expression

- \frac{1}{3 6}

Multiply by the Conjugate

\frac{- 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{- 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{- 3 36}{6}

Calculate

- \frac{3 36}{6}

c = - \frac{3 36}{6}

c = 0 c = - \frac{3 36}{6}

Solution

c_{1} = - \frac{3 36}{6}, c_{2} = 0

Alternative Form

c_{1} \approx - 0.550321, c_{2} = 0

Show Solution