Solve -2x^3 x^2 8x-16

Question

Simplify the expression

- 16 x^{6} - 16

Evaluate

- 2 x^{3} \times x^{2} \times 8 x - 16

Solution

More Steps

Evaluate

- 2 x^{3} \times x^{2} \times 8 x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 16 x^{3 + 2 + 1}

Add the numbers

- 16 x^{6}

- 16 x^{6} - 16

Show Solution

Factor the expression

- 16 (x^{2} + 1) (x^{4} - x^{2} + 1)

Evaluate

- 2 x^{3} \times x^{2} \times 8 x - 16

Evaluate

More Steps

Evaluate

- 2 x^{3} \times x^{2} \times 8 x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 16 x^{3 + 2 + 1}

Add the numbers

- 16 x^{6}

- 16 x^{6} - 16

Factor out - 16 from the expression

- 16 (x^{6} + 1)

Solution

More Steps

Evaluate

x^{6} + 1

Rewrite the expression in exponential form

x^{6} + 1^{3}

Use a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) to factor the expression

(x^{2} + 1) (x^{4} - x^{2} \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(x^{2} + 1) (x^{4} - x^{2} + 1^{2})

1 raised to any power equals to 1

(x^{2} + 1) (x^{4} - x^{2} + 1)

- 16 (x^{2} + 1) (x^{4} - x^{2} + 1)

Show Solution

Find the roots

x_{1} = - \frac{3}{2} - \frac{1}{2} i, x_{2} = \frac{3}{2} + \frac{1}{2} i

Alternative Form

x_{1} \approx - 0.866025 - 0.5 i, x_{2} \approx 0.866025 + 0.5 i

Evaluate

- 2 x^{3} \times x^{2} \times 8 x - 16

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

- 2 x^{3} \times x^{2} \times 8 x - 16 = 0

Multiply

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Multiply the terms

- 2 x^{3} \times x^{2} \times 8 x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 16 x^{3 + 2 + 1}

Add the numbers

- 16 x^{6}

- 16 x^{6} - 16 = 0

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

- 16 x^{6} = 0 + 16

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

- 16 x^{6} = 16

Change the signs on both sides of the equation

16 x^{6} = - 16

Divide both sides

\frac{16 x ^{6}}{16} = \frac{- 16}{16}

Divide the numbers

x^{6} = \frac{- 16}{16}

Divide the numbers

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Evaluate

\frac{- 16}{16}

Reduce the numbers

\frac{- 1}{1}

Calculate

- 1

x^{6} = - 1

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

x = \pm 6 - 1

Simplify the expression

More Steps

Evaluate

6 - 1

Rewrite the expression

1 \times (\frac{3}{2} + \frac{1}{2} i)

Any expression multiplied by 1 remains the same

\frac{3}{2} + \frac{1}{2} i

x = \pm (\frac{3}{2} + \frac{1}{2} i)

Separate the equation into 2 possible cases

x = \frac{3}{2} + \frac{1}{2} i x = - \frac{3}{2} - \frac{1}{2} i

Solution

x_{1} = - \frac{3}{2} - \frac{1}{2} i, x_{2} = \frac{3}{2} + \frac{1}{2} i

Alternative Form

x_{1} \approx - 0.866025 - 0.5 i, x_{2} \approx 0.866025 + 0.5 i

Show Solution