Solve -x^4 8x^2-16

Question

Simplify the expression

- 8 x^{6} - 16

Evaluate

- x^{4} \times 8 x^{2} - 16

Solution

More Steps

Evaluate

- x^{4} \times 8 x^{2}

Multiply the terms with the same base by adding their exponents

- x^{4 + 2} \times 8

Add the numbers

- x^{6} \times 8

Use the commutative property to reorder the terms

- 8 x^{6}

- 8 x^{6} - 16

Show Solution

Factor the expression

- 8 (x^{6} + 2)

Evaluate

- x^{4} \times 8 x^{2} - 16

Multiply

More Steps

Evaluate

x^{4} \times 8 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 8

Add the numbers

x^{6} \times 8

Use the commutative property to reorder the terms

8 x^{6}

- 8 x^{6} - 16

Solution

- 8 (x^{6} + 2)

Show Solution

Find the roots

x_{1} = - \frac{6 54}{2} - \frac{6 2}{2} i, x_{2} = \frac{6 54}{2} + \frac{6 2}{2} i

Alternative Form

x_{1} \approx - 0.972081 - 0.561231 i, x_{2} \approx 0.972081 + 0.561231 i

Evaluate

- x^{4} \times 8 x^{2} - 16

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

- x^{4} \times 8 x^{2} - 16 = 0

Multiply

More Steps

Multiply the terms

x^{4} \times 8 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 8

Add the numbers

x^{6} \times 8

Use the commutative property to reorder the terms

8 x^{6}

- 8 x^{6} - 16 = 0

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

- 8 x^{6} = 0 + 16

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

- 8 x^{6} = 16

Change the signs on both sides of the equation

8 x^{6} = - 16

Divide both sides

\frac{8 x ^{6}}{8} = \frac{- 16}{8}

Divide the numbers

x^{6} = \frac{- 16}{8}

Divide the numbers

More Steps

Evaluate

\frac{- 16}{8}

Reduce the numbers

\frac{- 2}{1}

Calculate

- 2

x^{6} = - 2

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

x = \pm 6 - 2

Simplify the expression

More Steps

Evaluate

6 - 2

Rewrite the expression

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

Apply the distributive property

62 \times \frac{3}{2} + 62 \times \frac{1}{2} i

Multiply the numbers

More Steps

Evaluate

62 \times \frac{3}{2}

Multiply the numbers

\frac{6 2 \times 3}{2}

Multiply the numbers

\frac{6 54}{2}

\frac{6 54}{2} + 62 \times \frac{1}{2} i

Multiply the numbers

\frac{6 54}{2} + \frac{6 2}{2} i

x = \pm (\frac{6 54}{2} + \frac{6 2}{2} i)

Separate the equation into 2 possible cases

x = \frac{6 54}{2} + \frac{6 2}{2} i x = - \frac{6 54}{2} - \frac{6 2}{2} i

Solution

x_{1} = - \frac{6 54}{2} - \frac{6 2}{2} i, x_{2} = \frac{6 54}{2} + \frac{6 2}{2} i

Alternative Form

x_{1} \approx - 0.972081 - 0.561231 i, x_{2} \approx 0.972081 + 0.561231 i

Show Solution