Solve x^(3)-x^(2) 3x^4

Question

Simplify the expression

x^{3} - 3 x^{6}

Evaluate

x^{3} - x^{2} \times 3 x^{4}

Solution

More Steps

Evaluate

x^{2} \times 3 x^{4}

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 3

Add the numbers

x^{6} \times 3

Use the commutative property to reorder the terms

3 x^{6}

x^{3} - 3 x^{6}

Show Solution

Factor the expression

x^{3} (1 - 3 x^{3})

Evaluate

x^{3} - x^{2} \times 3 x^{4}

Multiply

More Steps

Evaluate

x^{2} \times 3 x^{4}

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 3

Add the numbers

x^{6} \times 3

Use the commutative property to reorder the terms

3 x^{6}

x^{3} - 3 x^{6}

Rewrite the expression

x^{3} - x^{3} \times 3 x^{3}

Solution

x^{3} (1 - 3 x^{3})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 9}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.693361

Evaluate

x^{3} - x^{2} \times 3 x^{4}

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

x^{3} - x^{2} \times 3 x^{4} = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x^{4}

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 3

Add the numbers

x^{6} \times 3

Use the commutative property to reorder the terms

3 x^{6}

x^{3} - 3 x^{6} = 0

Factor the expression

x^{3} (1 - 3 x^{3}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 1 - 3 x^{3} = 0

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

x = 0 1 - 3 x^{3} = 0

Solve the equation

More Steps

Evaluate

1 - 3 x^{3} = 0

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

- 3 x^{3} = 0 - 1

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

- 3 x^{3} = - 1

Change the signs on both sides of the equation

3 x^{3} = 1

Divide both sides

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

Divide the numbers

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

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

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

Calculate

x = 3 \frac{1}{3}

Simplify the root

More Steps

Evaluate

3 \frac{1}{3}

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

\frac{3 1}{3 3}

Simplify the radical expression

\frac{1}{3 3}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{3 9}{3}

x = \frac{3 9}{3}

x = 0 x = \frac{3 9}{3}

Solution

x_{1} = 0, x_{2} = \frac{3 9}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.693361

Show Solution