Solve -10p-7p^4p - ScanMath

Question

Simplify the expression

- 10 p - 7 p^{5}

Evaluate

- 10 p - 7 p^{4} \times p

Solution

More Steps

Evaluate

7 p^{4} \times p

Multiply the terms with the same base by adding their exponents

7 p^{4 + 1}

Add the numbers

7 p^{5}

- 10 p - 7 p^{5}

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Factor the expression

- p (10 + 7 p^{4})

Evaluate

- 10 p - 7 p^{4} \times p

Multiply

More Steps

Evaluate

7 p^{4} \times p

Multiply the terms with the same base by adding their exponents

7 p^{4 + 1}

Add the numbers

7 p^{5}

- 10 p - 7 p^{5}

Rewrite the expression

- p \times 10 - p \times 7 p^{4}

Solution

- p (10 + 7 p^{4})

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Find the roots

p_{1} = - \frac{4 13720}{14} - \frac{4 13720}{14} i, p_{2} = \frac{4 13720}{14} + \frac{4 13720}{14} i, p_{3} = 0

Alternative Form

p_{1} \approx - 0.773055 - 0.773055 i, p_{2} \approx 0.773055 + 0.773055 i, p_{3} = 0

Evaluate

- 10 p - 7 p^{4} \times p

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

- 10 p - 7 p^{4} \times p = 0

Multiply

More Steps

Multiply the terms

7 p^{4} \times p

Multiply the terms with the same base by adding their exponents

7 p^{4 + 1}

Add the numbers

7 p^{5}

- 10 p - 7 p^{5} = 0

Factor the expression

- p (10 + 7 p^{4}) = 0

Divide both sides

p (10 + 7 p^{4}) = 0

Separate the equation into 2 possible cases

p = 0 10 + 7 p^{4} = 0

Solve the equation

More Steps

Evaluate

10 + 7 p^{4} = 0

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

7 p^{4} = 0 - 10

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

7 p^{4} = - 10

Divide both sides

\frac{7 p ^{4}}{7} = \frac{- 10}{7}

Divide the numbers

p^{4} = \frac{- 10}{7}

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

p^{4} = - \frac{10}{7}

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

p = \pm 4 - \frac{10}{7}

Simplify the expression

More Steps

Evaluate

4 - \frac{10}{7}

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

\frac{4 - 10}{4 7}

Simplify the radical expression

\frac{\frac{4 40}{2} + \frac{4 40}{2} i}{4 7}

Simplify

\frac{4 40}{2 4 7} + \frac{4 40}{2 4 7} i

Rearrange the numbers

\frac{4 13720}{14} + \frac{4 40}{2 4 7} i

Rearrange the numbers

\frac{4 13720}{14} + \frac{4 13720}{14} i

p = \pm (\frac{4 13720}{14} + \frac{4 13720}{14} i)

Separate the equation into 2 possible cases

p = \frac{4 13720}{14} + \frac{4 13720}{14} i p = - \frac{4 13720}{14} - \frac{4 13720}{14} i

p = 0 p = \frac{4 13720}{14} + \frac{4 13720}{14} i p = - \frac{4 13720}{14} - \frac{4 13720}{14} i

Solution

p_{1} = - \frac{4 13720}{14} - \frac{4 13720}{14} i, p_{2} = \frac{4 13720}{14} + \frac{4 13720}{14} i, p_{3} = 0

Alternative Form

p_{1} \approx - 0.773055 - 0.773055 i, p_{2} \approx 0.773055 + 0.773055 i, p_{3} = 0

Show Solution