Solve 3x^36x^2 -36x 1

Question

Simplify the expression

18 x^{5} - 36 x

Evaluate

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{3 + 2}

Add the numbers

18 x^{5}

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

Solution

18 x^{5} - 36 x

Show Solution

18 x (x^{4} - 2)

Evaluate

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{3 + 2}

Add the numbers

18 x^{5}

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

Multiply the terms

18 x^{5} - 36 x

Rewrite the expression

18 x \times x^{4} - 18 x \times 2

Solution

18 x (x^{4} - 2)

Show Solution

x_{1} = - 42, x_{2} = 0, x_{3} = 42

Alternative Form

x_{1} \approx - 1.189207, x_{2} = 0, x_{3} \approx 1.189207

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{3 + 2}

Add the numbers

18 x^{5}

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

Multiply the terms

18 x^{5} - 36 x = 0

Factor the expression

18 x (x^{4} - 2) = 0

Divide both sides

x (x^{4} - 2) = 0

Separate the equation into 2 possible cases

x = 0 x^{4} - 2 = 0

Solve the equation

More Steps

Evaluate

x^{4} - 2 = 0

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

x^{4} = 0 + 2

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

x^{4} = 2

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

x = \pm 42

Separate the equation into 2 possible cases

x = 42 x = - 42

x = 0 x = 42 x = - 42

Solution

x_{1} = - 42, x_{2} = 0, x_{3} = 42

Alternative Form

x_{1} \approx - 1.189207, x_{2} = 0, x_{3} \approx 1.189207

Show Solution