Solve x^36x^2 -36x 1

Question

x^{3} \times 6 x^{2} - 36 x \times 1

Simplify the expression

6 x^{5} - 36 x

Evaluate

x^{3} \times 6 x^{2} - 36 x \times 1

Multiply

More Steps

Multiply the terms

x^{3} \times 6 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 6

Add the numbers

x^{5} \times 6

Use the commutative property to reorder the terms

6 x^{5}

6 x^{5} - 36 x \times 1

Solution

6 x^{5} - 36 x

Show Solution

6 x (x^{4} - 6)

Evaluate

x^{3} \times 6 x^{2} - 36 x \times 1

Multiply

More Steps

Multiply the terms

x^{3} \times 6 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 6

Add the numbers

x^{5} \times 6

Use the commutative property to reorder the terms

6 x^{5}

6 x^{5} - 36 x \times 1

Multiply the terms

6 x^{5} - 36 x

Rewrite the expression

6 x \times x^{4} - 6 x \times 6

Solution

6 x (x^{4} - 6)

Show Solution

x_{1} = - 46, x_{2} = 0, x_{3} = 46

Alternative Form

x_{1} \approx - 1.565085, x_{2} = 0, x_{3} \approx 1.565085

Evaluate

x^{3} \times 6 x^{2} - 36 x \times 1

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

x^{3} \times 6 x^{2} - 36 x \times 1 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 6 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 6

Add the numbers

x^{5} \times 6

Use the commutative property to reorder the terms

6 x^{5}

6 x^{5} - 36 x \times 1 = 0

Multiply the terms

6 x^{5} - 36 x = 0

Factor the expression

6 x (x^{4} - 6) = 0

Divide both sides

x (x^{4} - 6) = 0

Separate the equation into 2 possible cases

x = 0 x^{4} - 6 = 0

Solve the equation

More Steps

Evaluate

x^{4} - 6 = 0

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

x^{4} = 0 + 6

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

x^{4} = 6

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 46

Separate the equation into 2 possible cases

x = 46 x = - 46

x = 0 x = 46 x = - 46

Solution

x_{1} = - 46, x_{2} = 0, x_{3} = 46

Alternative Form

x_{1} \approx - 1.565085, x_{2} = 0, x_{3} \approx 1.565085

Show Solution