Solve 42-21-31 n^69-39-36

Question

Simplify the expression

- 54 - 279 n^{6}

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- 9 (6 + 31 n^{6})

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n_{1} = - \frac{6 162 \times 3 1 ^{5}}{62} - \frac{6 6 \times 3 1 ^{5}}{62} i, n_{2} = \frac{6 162 \times 3 1 ^{5}}{62} + \frac{6 6 \times 3 1 ^{5}}{62} i

Alternative Form

n_{1} \approx - 0.658661 - 0.380278 i, n_{2} \approx 0.658661 + 0.380278 i

Evaluate

42 - 21 - 31 n^{6} \times 9 - 39 - 36

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

42 - 21 - 31 n^{6} \times 9 - 39 - 36 = 0

Multiply the terms

42 - 21 - 279 n^{6} - 39 - 36 = 0

Subtract the numbers

21 - 279 n^{6} - 39 - 36 = 0

Subtract the numbers

- 18 - 279 n^{6} - 36 = 0

Subtract the numbers

- 54 - 279 n^{6} = 0

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

- 279 n^{6} = 0 + 54

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

- 279 n^{6} = 54

Change the signs on both sides of the equation

279 n^{6} = - 54

Divide both sides

\frac{279 n ^{6}}{279} = \frac{- 54}{279}

Divide the numbers

n^{6} = \frac{- 54}{279}

Divide the numbers

More Steps

n^{6} = - \frac{6}{31}

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

n = \pm 6 - \frac{6}{31}

Simplify the expression

More Steps

n = \pm (\frac{6 162 \times 3 1 ^{5}}{62} + \frac{6 6 \times 3 1 ^{5}}{62} i)

Separate the equation into 2 possible cases

n = \frac{6 162 \times 3 1 ^{5}}{62} + \frac{6 6 \times 3 1 ^{5}}{62} i n = - \frac{6 162 \times 3 1 ^{5}}{62} - \frac{6 6 \times 3 1 ^{5}}{62} i

Solution

n_{1} = - \frac{6 162 \times 3 1 ^{5}}{62} - \frac{6 6 \times 3 1 ^{5}}{62} i, n_{2} = \frac{6 162 \times 3 1 ^{5}}{62} + \frac{6 6 \times 3 1 ^{5}}{62} i

Alternative Form

n_{1} \approx - 0.658661 - 0.380278 i, n_{2} \approx 0.658661 + 0.380278 i

Show Solution