Solve -1/2*3-4x^5 3/2x

Question

Simplify the expression

- \frac{3}{2} - 6 x^{6}

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- \frac{3}{2} (1 + 4 x^{6})

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x_{1} = - \frac{6 432}{4} + \frac{3 4}{4} i, x_{2} = \frac{6 432}{4} - \frac{3 4}{4} i

Alternative Form

x_{1} \approx - 0.687365 + 0.39685 i, x_{2} \approx 0.687365 - 0.39685 i

Evaluate

- \frac{1}{2} \times 3 - 4 x^{5} \times \frac{3}{2} x

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

- \frac{1}{2} \times 3 - 4 x^{5} \times \frac{3}{2} x = 0

Multiply the numbers

- \frac{3}{2} - 4 x^{5} \times \frac{3}{2} x = 0

Multiply

More Steps

- \frac{3}{2} - 6 x^{6} = 0

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

- 6 x^{6} = 0 + \frac{3}{2}

Add the terms

- 6 x^{6} = \frac{3}{2}

Change the signs on both sides of the equation

6 x^{6} = - \frac{3}{2}

Multiply by the reciprocal

6 x^{6} \times \frac{1}{6} = - \frac{3}{2} \times \frac{1}{6}

Multiply

x^{6} = - \frac{3}{2} \times \frac{1}{6}

Multiply

More Steps

x^{6} = - \frac{1}{4}

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

x = \pm 6 - \frac{1}{4}

Simplify the expression

More Steps

x = \pm (\frac{6 432}{2 ^{2}} - \frac{3 4}{4} i)

Separate the equation into 2 possible cases

x = \frac{6 432}{2 ^{2}} - \frac{3 4}{4} i x = - \frac{6 432}{2 ^{2}} + \frac{3 4}{4} i

Calculate

x = \frac{6 432}{4} - \frac{3 4}{4} i x = - \frac{6 432}{2 ^{2}} + \frac{3 4}{4} i

Calculate

x = \frac{6 432}{4} - \frac{3 4}{4} i x = - \frac{6 432}{4} + \frac{3 4}{4} i

Solution

x_{1} = - \frac{6 432}{4} + \frac{3 4}{4} i, x_{2} = \frac{6 432}{4} - \frac{3 4}{4} i

Alternative Form

x_{1} \approx - 0.687365 + 0.39685 i, x_{2} \approx 0.687365 - 0.39685 i

Show Solution