Solve x (11x-5) (6x^5)

Question

Simplify the expression

66 x^{7} - 30 x^{6}

Evaluate

x (11 x - 5) \times 6 x^{5}

Multiply the terms with the same base by adding their exponents

x^{1 + 5} (11 x - 5) \times 6

Add the numbers

x^{6} (11 x - 5) \times 6

Use the commutative property to reorder the terms

6 x^{6} (11 x - 5)

Apply the distributive property

6 x^{6} \times 11 x - 6 x^{6} \times 5

Multiply the terms

More Steps

Evaluate

6 x^{6} \times 11 x

Multiply the numbers

66 x^{6} \times x

Multiply the terms

More Steps

Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

66 x^{7}

66 x^{7} - 6 x^{6} \times 5

Solution

66 x^{7} - 30 x^{6}

Show Solution

x_{1} = 0, x_{2} = \frac{5}{11}

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{4} \dot{5}

Evaluate

x (11 x - 5) (6 x^{5})

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

x (11 x - 5) (6 x^{5}) = 0

Multiply the terms

x (11 x - 5) \times 6 x^{5} = 0

Multiply

More Steps

Multiply the terms

x (11 x - 5) \times 6 x^{5}

Multiply the terms with the same base by adding their exponents

x^{1 + 5} (11 x - 5) \times 6

Add the numbers

x^{6} (11 x - 5) \times 6

Use the commutative property to reorder the terms

6 x^{6} (11 x - 5)

6 x^{6} (11 x - 5) = 0

Elimination the left coefficient

x^{6} (11 x - 5) = 0

Separate the equation into 2 possible cases

x^{6} = 0 11 x - 5 = 0

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

x = 0 11 x - 5 = 0

Solve the equation

More Steps

Evaluate

11 x - 5 = 0

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

11 x = 0 + 5

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

11 x = 5

Divide both sides

\frac{11 x}{11} = \frac{5}{11}

Divide the numbers

x = \frac{5}{11}

x = 0 x = \frac{5}{11}

Solution

x_{1} = 0, x_{2} = \frac{5}{11}

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{4} \dot{5}

Show Solution