Solve -x^3(x 1) - 1

Question

Simplify the expression

- x^{4} - 1

Evaluate

- x^{3} (x \times 1) - 1

Remove the parentheses

- x^{3} \times x \times 1 - 1

Solution

More Steps

Evaluate

- x^{3} \times x \times 1

Rewrite the expression

- x^{3} \times x

Multiply the terms with the same base by adding their exponents

- x^{3 + 1}

Add the numbers

- x^{4}

- x^{4} - 1

Show Solution

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

Alternative Form

x_{1} \approx - 0.707107 - 0.707107 i, x_{2} \approx 0.707107 + 0.707107 i

Evaluate

- x^{3} (x \times 1) - 1

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

- x^{3} (x \times 1) - 1 = 0

Any expression multiplied by 1 remains the same

- x^{3} \times x - 1 = 0

Multiply the terms

More Steps

Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

- x^{4} - 1 = 0

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

- x^{4} = 0 + 1

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

- x^{4} = 1

Change the signs on both sides of the equation

x^{4} = - 1

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

x = \pm 4 - 1

Simplify the expression

More Steps

Evaluate

4 - 1

Rewrite the expression

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

Any expression multiplied by 1 remains the same

\frac{2}{2} + \frac{2}{2} i

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

x_{1} \approx - 0.707107 - 0.707107 i, x_{2} \approx 0.707107 + 0.707107 i

Show Solution