Solve -8x 10x^3x - 7x

Question

Simplify the expression

- 80 x^{5} - 7 x

Evaluate

- 8 x \times 10 x^{3} \times x - 7 x

Solution

More Steps

Evaluate

- 8 x \times 10 x^{3} \times x

Multiply the terms

- 80 x \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

- 80 x^{1 + 3 + 1}

Add the numbers

- 80 x^{5}

- 80 x^{5} - 7 x

Show Solution

Factor the expression

- x (80 x^{4} + 7)

Evaluate

- 8 x \times 10 x^{3} \times x - 7 x

Multiply

More Steps

Evaluate

- 8 x \times 10 x^{3} \times x

Multiply the terms

- 80 x \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

- 80 x^{1 + 3 + 1}

Add the numbers

- 80 x^{5}

- 80 x^{5} - 7 x

Rewrite the expression

- x \times 80 x^{4} - x \times 7

Solution

- x (80 x^{4} + 7)

Show Solution

Find the roots

x_{1} = - \frac{4 3500}{20} - \frac{4 3500}{20} i, x_{2} = \frac{4 3500}{20} + \frac{4 3500}{20} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.38458 - 0.38458 i, x_{2} \approx 0.38458 + 0.38458 i, x_{3} = 0

Evaluate

- 8 x \times 10 x^{3} \times x - 7 x

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

- 8 x \times 10 x^{3} \times x - 7 x = 0

Multiply

More Steps

Multiply the terms

- 8 x \times 10 x^{3} \times x

Multiply the terms

- 80 x \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

- 80 x^{1 + 3 + 1}

Add the numbers

- 80 x^{5}

- 80 x^{5} - 7 x = 0

Factor the expression

- x (80 x^{4} + 7) = 0

Divide both sides

x (80 x^{4} + 7) = 0

Separate the equation into 2 possible cases

x = 0 80 x^{4} + 7 = 0

Solve the equation

More Steps

Evaluate

80 x^{4} + 7 = 0

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

80 x^{4} = 0 - 7

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

80 x^{4} = - 7

Divide both sides

\frac{80 x ^{4}}{80} = \frac{- 7}{80}

Divide the numbers

x^{4} = \frac{- 7}{80}

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

x^{4} = - \frac{7}{80}

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

x = \pm 4 - \frac{7}{80}

Simplify the expression

More Steps

Evaluate

4 - \frac{7}{80}

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

\frac{4 - 7}{4 80}

Simplify the radical expression

\frac{\frac{4 28}{2} + \frac{4 28}{2} i}{4 80}

Simplify the radical expression

\frac{\frac{4 28}{2} + \frac{4 28}{2} i}{2 4 5}

Simplify

\frac{4 28}{4 4 5} + \frac{4 28}{4 4 5} i

Rearrange the numbers

\frac{4 3500}{20} + \frac{4 28}{4 4 5} i

Rearrange the numbers

\frac{4 3500}{20} + \frac{4 3500}{20} i

x = \pm (\frac{4 3500}{20} + \frac{4 3500}{20} i)

Separate the equation into 2 possible cases

x = \frac{4 3500}{20} + \frac{4 3500}{20} i x = - \frac{4 3500}{20} - \frac{4 3500}{20} i

x = 0 x = \frac{4 3500}{20} + \frac{4 3500}{20} i x = - \frac{4 3500}{20} - \frac{4 3500}{20} i

Solution

x_{1} = - \frac{4 3500}{20} - \frac{4 3500}{20} i, x_{2} = \frac{4 3500}{20} + \frac{4 3500}{20} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.38458 - 0.38458 i, x_{2} \approx 0.38458 + 0.38458 i, x_{3} = 0

Show Solution