Solve -6 (9x^5) - 3x^4x = -408 x

Question

Solve the equation

x_{1} = - \frac{4 932824}{19}, x_{2} = 0, x_{3} = \frac{4 932824}{19}

Alternative Form

x_{1} \approx - 1.635672, x_{2} = 0, x_{3} \approx 1.635672

Evaluate

- 6 \times 9 x^{5} - 3 x^{4} \times x = - 408 x

Simplify

More Steps

Evaluate

- 6 \times 9 x^{5} - 3 x^{4} \times x

Multiply the numbers

- 54 x^{5} - 3 x^{4} \times x

Multiply

More Steps

Multiply the terms

3 x^{4} \times x

Multiply the terms with the same base by adding their exponents

3 x^{4 + 1}

Add the numbers

3 x^{5}

- 54 x^{5} - 3 x^{5}

Collect like terms by calculating the sum or difference of their coefficients

(- 54 - 3) x^{5}

Subtract the numbers

- 57 x^{5}

- 57 x^{5} = - 408 x

Add or subtract both sides

- 57 x^{5} - (- 408 x) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 57 x^{5} + 408 x = 0

Factor the expression

3 x (- 19 x^{4} + 136) = 0

Divide both sides

x (- 19 x^{4} + 136) = 0

Separate the equation into 2 possible cases

x = 0 - 19 x^{4} + 136 = 0

Solve the equation

More Steps

Evaluate

- 19 x^{4} + 136 = 0

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

- 19 x^{4} = 0 - 136

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

- 19 x^{4} = - 136

Change the signs on both sides of the equation

19 x^{4} = 136

Divide both sides

\frac{19 x ^{4}}{19} = \frac{136}{19}

Divide the numbers

x^{4} = \frac{136}{19}

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

x = \pm 4 \frac{136}{19}

Simplify the expression

More Steps

Evaluate

4 \frac{136}{19}

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

\frac{4 136}{4 19}

Multiply by the Conjugate

\frac{4 136 \times 4 1 9 ^{3}}{4 19 \times 4 1 9 ^{3}}

Simplify

\frac{4 136 \times 4 6859}{4 19 \times 4 1 9 ^{3}}

Multiply the numbers

\frac{4 932824}{4 19 \times 4 1 9 ^{3}}

Multiply the numbers

\frac{4 932824}{19}

x = \pm \frac{4 932824}{19}

Separate the equation into 2 possible cases

x = \frac{4 932824}{19} x = - \frac{4 932824}{19}

x = 0 x = \frac{4 932824}{19} x = - \frac{4 932824}{19}

Solution

x_{1} = - \frac{4 932824}{19}, x_{2} = 0, x_{3} = \frac{4 932824}{19}

Alternative Form

x_{1} \approx - 1.635672, x_{2} = 0, x_{3} \approx 1.635672

Show Solution

Solve the equation

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