Solve 105x-(100x^5)

Question

Factor the expression

5 x (21 - 20 x^{4})

Evaluate

105 x - 100 x^{5}

Rewrite the expression

5 x \times 21 - 5 x \times 20 x^{4}

Solution

5 x (21 - 20 x^{4})

Show Solution

x_{1} = - \frac{4 10500}{10}, x_{2} = 0, x_{3} = \frac{4 10500}{10}

Alternative Form

x_{1} \approx - 1.012272, x_{2} = 0, x_{3} \approx 1.012272

Evaluate

105 x - (100 x^{5})

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

105 x - (100 x^{5}) = 0

Multiply the terms

105 x - 100 x^{5} = 0

Factor the expression

5 x (21 - 20 x^{4}) = 0

Divide both sides

x (21 - 20 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 21 - 20 x^{4} = 0

Solve the equation

More Steps

Evaluate

21 - 20 x^{4} = 0

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

- 20 x^{4} = 0 - 21

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

- 20 x^{4} = - 21

Change the signs on both sides of the equation

20 x^{4} = 21

Divide both sides

\frac{20 x ^{4}}{20} = \frac{21}{20}

Divide the numbers

x^{4} = \frac{21}{20}

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

x = \pm 4 \frac{21}{20}

Simplify the expression

More Steps

Evaluate

4 \frac{21}{20}

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

\frac{4 21}{4 20}

Multiply by the Conjugate

\frac{4 21 \times 4 2 0 ^{3}}{4 20 \times 4 2 0 ^{3}}

Simplify

\frac{4 21 \times 2 4 500}{4 20 \times 4 2 0 ^{3}}

Multiply the numbers

\frac{2 4 10500}{4 20 \times 4 2 0 ^{3}}

Multiply the numbers

\frac{2 4 10500}{20}

Cancel out the common factor 2

\frac{4 10500}{10}

x = \pm \frac{4 10500}{10}

Separate the equation into 2 possible cases

x = \frac{4 10500}{10} x = - \frac{4 10500}{10}

x = 0 x = \frac{4 10500}{10} x = - \frac{4 10500}{10}

Solution

x_{1} = - \frac{4 10500}{10}, x_{2} = 0, x_{3} = \frac{4 10500}{10}

Alternative Form

x_{1} \approx - 1.012272, x_{2} = 0, x_{3} \approx 1.012272

Show Solution