Solve x^(4)-2x^(3) 8x-16

Question

Simplify the expression

- 15 x^{4} - 16

Show Solution

x_{1} = - \frac{4 13500}{15} - \frac{4 13500}{15} i, x_{2} = \frac{4 13500}{15} + \frac{4 13500}{15} i

Alternative Form

x_{1} \approx - 0.718608 - 0.718608 i, x_{2} \approx 0.718608 + 0.718608 i

Evaluate

x^{4} - 2 x^{3} \times 8 x - 16

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

x^{4} - 2 x^{3} \times 8 x - 16 = 0

Multiply

More Steps

x^{4} - 16 x^{4} - 16 = 0

Subtract the terms

More Steps

- 15 x^{4} - 16 = 0

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

- 15 x^{4} = 0 + 16

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

- 15 x^{4} = 16

Change the signs on both sides of the equation

15 x^{4} = - 16

Divide both sides

\frac{15 x ^{4}}{15} = \frac{- 16}{15}

Divide the numbers

x^{4} = \frac{- 16}{15}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{4} = - \frac{16}{15}

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

x = \pm 4 - \frac{16}{15}

Simplify the expression

More Steps

x = \pm (\frac{4 13500}{15} + \frac{4 13500}{15} i)

Separate the equation into 2 possible cases

x = \frac{4 13500}{15} + \frac{4 13500}{15} i x = - \frac{4 13500}{15} - \frac{4 13500}{15} i

Solution

x_{1} = - \frac{4 13500}{15} - \frac{4 13500}{15} i, x_{2} = \frac{4 13500}{15} + \frac{4 13500}{15} i

Alternative Form

x_{1} \approx - 0.718608 - 0.718608 i, x_{2} \approx 0.718608 + 0.718608 i

Show Solution