Solve 3x^6 - 2x = -3x^6

Question

Solve the equation

x_{1} = 0, x_{2} = \frac{5 81}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.802742

Evaluate

3 x^{6} - 2 x = - 3 x^{6}

Move the expression to the left side

3 x^{6} - 2 x - (- 3 x^{6}) = 0

Subtract the terms

More Steps

Evaluate

3 x^{6} - 2 x - (- 3 x^{6})

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

3 x^{6} - 2 x + 3 x^{6}

Add the terms

More Steps

Evaluate

3 x^{6} + 3 x^{6}

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

(3 + 3) x^{6}

Add the numbers

6 x^{6}

6 x^{6} - 2 x

6 x^{6} - 2 x = 0

Factor the expression

2 x (3 x^{5} - 1) = 0

Divide both sides

x (3 x^{5} - 1) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{5} - 1 = 0

Solve the equation

More Steps

Evaluate

3 x^{5} - 1 = 0

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

3 x^{5} = 0 + 1

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

3 x^{5} = 1

Divide both sides

\frac{3 x ^{5}}{3} = \frac{1}{3}

Divide the numbers

x^{5} = \frac{1}{3}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{3}

Calculate

x = 5 \frac{1}{3}

Simplify the root

More Steps

Evaluate

5 \frac{1}{3}

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

\frac{5 1}{5 3}

Simplify the radical expression

\frac{1}{5 3}

Multiply by the Conjugate

\frac{5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

\frac{5 81}{3}

x = \frac{5 81}{3}

x = 0 x = \frac{5 81}{3}

Solution

x_{1} = 0, x_{2} = \frac{5 81}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.802742

Show Solution

Solve the equation

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