Solve 3x - 212x^5

Question

Factor the expression

x (3 - 212 x^{4})

Evaluate

3 x - 212 x^{5}

Rewrite the expression

x \times 3 - x \times 212 x^{4}

Solution

x (3 - 212 x^{4})

Show Solution

x_{1} = - \frac{4 3 \times 21 2 ^{3}}{212}, x_{2} = 0, x_{3} = \frac{4 3 \times 21 2 ^{3}}{212}

Alternative Form

x_{1} \approx - 0.344903, x_{2} = 0, x_{3} \approx 0.344903

Evaluate

3 x - 212 x^{5}

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

3 x - 212 x^{5} = 0

Factor the expression

x (3 - 212 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 3 - 212 x^{4} = 0

Solve the equation

More Steps

Evaluate

3 - 212 x^{4} = 0

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

- 212 x^{4} = 0 - 3

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

- 212 x^{4} = - 3

Change the signs on both sides of the equation

212 x^{4} = 3

Divide both sides

\frac{212 x ^{4}}{212} = \frac{3}{212}

Divide the numbers

x^{4} = \frac{3}{212}

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

x = \pm 4 \frac{3}{212}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{212}

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

\frac{4 3}{4 212}

Multiply by the Conjugate

\frac{4 3 \times 4 21 2 ^{3}}{4 212 \times 4 21 2 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 3 \times 21 2 ^{3}}{4 212 \times 4 21 2 ^{3}}

Multiply the numbers

\frac{4 3 \times 21 2 ^{3}}{212}

x = \pm \frac{4 3 \times 21 2 ^{3}}{212}

Separate the equation into 2 possible cases

x = \frac{4 3 \times 21 2 ^{3}}{212} x = - \frac{4 3 \times 21 2 ^{3}}{212}

x = 0 x = \frac{4 3 \times 21 2 ^{3}}{212} x = - \frac{4 3 \times 21 2 ^{3}}{212}

Solution

x_{1} = - \frac{4 3 \times 21 2 ^{3}}{212}, x_{2} = 0, x_{3} = \frac{4 3 \times 21 2 ^{3}}{212}

Alternative Form

x_{1} \approx - 0.344903, x_{2} = 0, x_{3} \approx 0.344903

Show Solution