Solve 8+3a 8a e a^3a

Question

Simplify the expression

8 + 24 e a^{6}

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8 (1 + 3 e a^{6})

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a_{1} = - \frac{6 9 e ^{5}}{2 e} + \frac{6 243 e ^{5}}{6 e} i, a_{2} = \frac{6 9 e ^{5}}{2 e} - \frac{6 243 e ^{5}}{6 e} i

Alternative Form

a_{1} \approx - 0.610419 + 0.352426 i, a_{2} \approx 0.610419 - 0.352426 i

Evaluate

8 + 3 a \times 8 a e a^{3} \times a

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

8 + 3 a \times 8 a e a^{3} \times a = 0

Multiply

More Steps

8 + 24 e a^{6} = 0

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

24 e a^{6} = 0 - 8

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

24 e a^{6} = - 8

Divide both sides

\frac{24 e a ^{6}}{24 e} = \frac{- 8}{24 e}

Divide the numbers

a^{6} = \frac{- 8}{24 e}

Divide the numbers

More Steps

a^{6} = - \frac{1}{3 e}

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

a = \pm 6 - \frac{1}{3 e}

Simplify the expression

More Steps

a = \pm (\frac{6 9 e ^{5}}{2 e} - \frac{6 243 e ^{5}}{6 e} i)

Separate the equation into 2 possible cases

a = \frac{6 9 e ^{5}}{2 e} - \frac{6 243 e ^{5}}{6 e} i a = - \frac{6 9 e ^{5}}{2 e} + \frac{6 243 e ^{5}}{6 e} i

Solution

a_{1} = - \frac{6 9 e ^{5}}{2 e} + \frac{6 243 e ^{5}}{6 e} i, a_{2} = \frac{6 9 e ^{5}}{2 e} - \frac{6 243 e ^{5}}{6 e} i

Alternative Form

a_{1} \approx - 0.610419 + 0.352426 i, a_{2} \approx 0.610419 - 0.352426 i

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