Solve x^6-9x^4 x^2-9

Question

Simplify the expression

- 8 x^{6} - 9

Show Solution

x_{1} = - \frac{6 1944}{4} - \frac{6 72}{4} i, x_{2} = \frac{6 1944}{4} + \frac{6 72}{4} i

Alternative Form

x_{1} \approx - 0.883194 - 0.509912 i, x_{2} \approx 0.883194 + 0.509912 i

Evaluate

x^{6} - 9 x^{4} \times x^{2} - 9

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

x^{6} - 9 x^{4} \times x^{2} - 9 = 0

Multiply

More Steps

x^{6} - 9 x^{6} - 9 = 0

Subtract the terms

More Steps

- 8 x^{6} - 9 = 0

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

- 8 x^{6} = 0 + 9

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

- 8 x^{6} = 9

Change the signs on both sides of the equation

8 x^{6} = - 9

Divide both sides

\frac{8 x ^{6}}{8} = \frac{- 9}{8}

Divide the numbers

x^{6} = \frac{- 9}{8}

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

x^{6} = - \frac{9}{8}

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

x = \pm 6 - \frac{9}{8}

Simplify the expression

More Steps

x = \pm (\frac{6 1944}{4} + \frac{6 72}{4} i)

Separate the equation into 2 possible cases

x = \frac{6 1944}{4} + \frac{6 72}{4} i x = - \frac{6 1944}{4} - \frac{6 72}{4} i

Solution

x_{1} = - \frac{6 1944}{4} - \frac{6 72}{4} i, x_{2} = \frac{6 1944}{4} + \frac{6 72}{4} i

Alternative Form

x_{1} \approx - 0.883194 - 0.509912 i, x_{2} \approx 0.883194 + 0.509912 i

Show Solution