Solve d+d^5e - ScanMath

Question

Simplify the expression

Solution

d + e d^{5}

Evaluate

d + d^{5} e

Solution

d + e d^{5}

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Factor

d (1 + e d^{4})

Evaluate

d + d^{5} e

Use the commutative property to reorder the terms

d + e d^{5}

Rewrite the expression

d + d e d^{4}

Solution

d (1 + e d^{4})

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Find the roots of the algebra expression

d_{1} = - \frac{4 4 e ^{3}}{2 e} + \frac{4 4 e ^{3}}{2 e} i, d_{2} = \frac{4 4 e ^{3}}{2 e} - \frac{4 4 e ^{3}}{2 e} i, d_{3} = 0

Alternative Form

d_{1} \approx - 0.550695 + 0.550695 i, d_{2} \approx 0.550695 - 0.550695 i, d_{3} = 0

Evaluate

d + d^{5} e

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

d + d^{5} e = 0

Use the commutative property to reorder the terms

d + e d^{5} = 0

Factor the expression

d (1 + e d^{4}) = 0

Separate the equation into 2 possible cases

d = 0 1 + e d^{4} = 0

Solve the equation

More Steps

Evaluate

1 + e d^{4} = 0

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

e d^{4} = 0 - 1

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

e d^{4} = - 1

Divide both sides

\frac{e d ^{4}}{e} = \frac{- 1}{e}

Divide the numbers

d^{4} = \frac{- 1}{e}

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

d^{4} = - \frac{1}{e}

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

d = \pm 4 - \frac{1}{e}

Simplify the expression

More Steps

Evaluate

4 - \frac{1}{e}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 1}{4 - e}

Simplify the radical expression

\frac{1}{4 - e}

Simplify the radical expression

\frac{1}{\frac{4 4 e}{2} + \frac{4 4 e}{2} i}

Multiply by the Conjugate

\frac{\frac{4 4 e}{2} - \frac{4 4 e}{2} i}{( \frac{4 4 e}{2} + \frac{4 4 e}{2} i ) ( \frac{4 4 e}{2} - \frac{4 4 e}{2} i )}

Calculate

\frac{\frac{4 4 e}{2} - \frac{4 4 e}{2} i}{e}

Simplify

\frac{4 4 e}{2 e} - \frac{4 4 e}{2 e} i

Rearrange the numbers

\frac{4 4 e ^{3}}{2 e} - \frac{4 4 e}{2 e} i

Rearrange the numbers

\frac{4 4 e ^{3}}{2 e} - \frac{4 4 e ^{3}}{2 e} i

d = \pm (\frac{4 4 e ^{3}}{2 e} - \frac{4 4 e ^{3}}{2 e} i)

Separate the equation into 2 possible cases

d = \frac{4 4 e ^{3}}{2 e} - \frac{4 4 e ^{3}}{2 e} i d = - \frac{4 4 e ^{3}}{2 e} + \frac{4 4 e ^{3}}{2 e} i

d = 0 d = \frac{4 4 e ^{3}}{2 e} - \frac{4 4 e ^{3}}{2 e} i d = - \frac{4 4 e ^{3}}{2 e} + \frac{4 4 e ^{3}}{2 e} i

Solution

d_{1} = - \frac{4 4 e ^{3}}{2 e} + \frac{4 4 e ^{3}}{2 e} i, d_{2} = \frac{4 4 e ^{3}}{2 e} - \frac{4 4 e ^{3}}{2 e} i, d_{3} = 0

Alternative Form

d_{1} \approx - 0.550695 + 0.550695 i, d_{2} \approx 0.550695 - 0.550695 i, d_{3} = 0

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