Solve 27x x^5 -12x ^3

Question

Simplify the expression

27 x^{6} - 12 x^{3}

Evaluate

27 x \times x^{5} - 12 x^{3}

Solution

More Steps

Evaluate

27 x \times x^{5}

Multiply the terms with the same base by adding their exponents

27 x^{1 + 5}

Add the numbers

27 x^{6}

27 x^{6} - 12 x^{3}

Show Solution

Factor the expression

3 x^{3} (9 x^{3} - 4)

Evaluate

27 x \times x^{5} - 12 x^{3}

Multiply

More Steps

Evaluate

27 x \times x^{5}

Multiply the terms with the same base by adding their exponents

27 x^{1 + 5}

Add the numbers

27 x^{6}

27 x^{6} - 12 x^{3}

Rewrite the expression

3 x^{3} \times 9 x^{3} - 3 x^{3} \times 4

Solution

3 x^{3} (9 x^{3} - 4)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 12}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.763143

Evaluate

27 x \times x^{5} - 12 x^{3}

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

27 x \times x^{5} - 12 x^{3} = 0

Multiply

More Steps

Multiply the terms

27 x \times x^{5}

Multiply the terms with the same base by adding their exponents

27 x^{1 + 5}

Add the numbers

27 x^{6}

27 x^{6} - 12 x^{3} = 0

Factor the expression

3 x^{3} (9 x^{3} - 4) = 0

Divide both sides

x^{3} (9 x^{3} - 4) = 0

Separate the equation into 2 possible cases

x^{3} = 0 9 x^{3} - 4 = 0

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

x = 0 9 x^{3} - 4 = 0

Solve the equation

More Steps

Evaluate

9 x^{3} - 4 = 0

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

9 x^{3} = 0 + 4

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

9 x^{3} = 4

Divide both sides

\frac{9 x ^{3}}{9} = \frac{4}{9}

Divide the numbers

x^{3} = \frac{4}{9}

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

3 x^{3} = 3 \frac{4}{9}

Calculate

x = 3 \frac{4}{9}

Simplify the root

More Steps

Evaluate

3 \frac{4}{9}

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

\frac{3 4}{3 9}

Multiply by the Conjugate

\frac{3 4 \times 3 9 ^{2}}{3 9 \times 3 9 ^{2}}

Simplify

\frac{3 4 \times 3 3 3}{3 9 \times 3 9 ^{2}}

Multiply the numbers

\frac{3 3 12}{3 9 \times 3 9 ^{2}}

Multiply the numbers

\frac{3 3 12}{3 ^{2}}

Reduce the fraction

\frac{3 12}{3}

x = \frac{3 12}{3}

x = 0 x = \frac{3 12}{3}

Solution

x_{1} = 0, x_{2} = \frac{3 12}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.763143

Show Solution